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Question 74205: I have the following problem:
Let P(n, k) denote the number of permutations of k objects selected from a set of n. We have the formula P (n,k) = n!/(n-k)!
Prove that for all integers n>or=2, P(n+1,2)-P(n, 2)=2P(n, 1).
I did some research on factorial identities and got a little further, but I'm not getting to the desired end result. I guess where I'm most stuck is the goal -- is 2P(n,1) equal to 2(n!/(n-1)!)? I've never seen the '2P' before. Thanks!

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Question 74411: A restaurant offers a choice of 3 appetizers, 6 main dishes, 7 desserts, and 5 beverages. How many complete dinners are available?
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Question 76118: A hand of 12 cards is dealt from a well- shuffled standard 52 card deck of cards. What is the probability that the hand contains 4 jacks?
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Question 76116: A coin is tossed 9 times. What is the probability that the coin will land heads at least 7 times?
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Question 76116: A coin is tossed 9 times. What is the probability that the coin will land heads at least 7 times?
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Question 76400: My question is about adding factorials. This seems easy but not sure.
Question is 9! + 4!

I understand that the nine is 9 8 7 6 5 4 3 2 1 then the 4 is 4 3 2 1 do you just add the numbers?????? Or what?
Thanks,
Gary
Click here to see answer by jim_thompson5910(35256)

Question 77763: I get10X 5040 =50400 is this right?
In how many ways can a phone number be created if there are ten ways that the first three digits can be arranged and then each of the remaining four digits canbe any digit from 0-9 as long as no digit is repeated in the group of 4?
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Question 80736: If the first three digits of someone's phone number (do not include area code) are 777, How many different phone numbers could they have?
Please don't just give me and answer. I would like to know how to work this problem.
I know that there 7digits in a phone numer, and the first three digits are taken then there are 4digits availiable.
is it P=n/(n-r)! where n=7 and r=4 I am not sure.
Click here to see answer by stanbon(75887)

Question 83527: In how many ways can 5 books be arranged on a shelf?
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Question 83529: A three-digit number is formed by selecting from the digits 1,2,3,4,5 and 6 with no repitition. How many of these three digit numbers will have a number greater than 300?
Click here to see answer by Edwin McCravy(20054)

Question 83645: In the four periods before lunch, Sally will take math, english, italian, and biology. In how many ways can Sally's program be arranged?
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Question 83646: In how many ways can we elect 11 students to be president and vice-president?
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Question 85109: 2.Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule?

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Question 85108: 1.How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)?

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Question 85114: How many seven-digit phone numbers can be formed if the first digit cannot be 0 and
a)repetition of digits is not permitted?
b)if repetition of digits is permitted?

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Question 85082: hey i need help with word probabilitiesfor example...
the letters a through z are written on pieces of paper and placed in a jar. Four of them are selected one after the other without replacing any of them.
and
how do you know how to do it.
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Question 85120: The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?

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Question 85123: Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
the first letter must be Y
the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first

Click here to see answer by jim_thompson5910(35256)

Question 85233: State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?

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Question 85232: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:
a.All the toppings are vegetables
b.All the toppings are meat
c.There is only cheese on the pizza
d.There are 2 vegetables, 1 meat and 1 cheese
e.There are 3 meats and 1 cheese.

Click here to see answer by stanbon(75887)

Question 85230: I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?

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Question 85229: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?

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Question 85182: State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?

Click here to see answer by scianci(186)

Question 85179: I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?

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Question 85468: Could you help me with this problem:
Evaluate 20!
Thanks!
Click here to see answer by jim_thompson5910(35256)

Question 85469: Please solve:
10 C 3
Thank you.
* the 10 and 3 of course are ment to be sub numbers
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Question 85484: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:
a.All the toppings are vegetables
b.All the toppings are meat
c.There is only cheese on the pizza
d.There are 2 vegetables, 1 meat and 1 cheese
e.There are 3 meats and 1 cheese.
: A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:
a.All the toppings are vegetables
b.All the toppings are meat
c.There is only cheese on the pizza
d.There are 2 vegetables, 1 meat and 1 cheese
e.There are 3 meats and 1 cheese.

Click here to see answer by checkley75(3666)

Question 85795: How many three-digit numbers can you form from the digits 1, 2, 3, 4, 5, 6 if:
a.) the digits can be repeated
b.) The digits can not be repeated
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Question 85794: Could you please assist me in solving this question?:
(3 points) Solve the following equation for n: nC2=100C98
Thank you,
Gary
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Question 85849: Please throughly explain how to solve this problem:
To win the Lotto in the state of Alabama, one must correctly select 6 numbers from a collection of 49 (1 through 49). This order in which the selection is made does not matter. How many different selections are possible?
Thanks
Click here to see answer by checkley75(3666)

Question 85850: Please help me find a solution to this problem
Blue-Bunny Ice Cream, sells 31 flavors.
A.) How many 2-dip cones are possible if order of flavors is to be considered and no flavor is repeated?
B.) How many 2-dip cones are possible if order of flavors is to be considered and flavors CAN be repeated.
C.) How many 2-dip cones are possible if order is NOT considered and NO flavor is repeated?
Thanks

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Question 86701: Can you please assist me with this?
In how many different orders can you arrange 4 vases on a bookcase self?
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Question 86700: May you help me in solving this problem? I'm afraid I don't even know what formula to use. I can't even find this section in my text book. Thanks!
Use these figures for 1999 resident U.S. population by age to answer this question:
AGE ------POPULATION (In Thousands)
0-19 ------75,791
20-39 ----81,004
40-59 ------62,383
75-84 -----11,145
85 and older ----3,628
A.) Find the Probability that the resident is under the age of 20.
B.) Find the Probability that the resident is in the 20-39 or 60-74 age group.
Click here to see answer by Flake(45)

Question 86973: PLEASE HELP ME...

A poker hand consists of 5 cards from a deck of 52 cards. How many different poker hands are possible which contain exactly 3 diamonds?

PLEASE HELP THANK YOU
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Question 87027: If someone has 6 different pairs of pants, 10 different shirts, and 5 different pair of shoes, how many different pant, shirt, and shoe outfits are possible?
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Question 87331: How many ways can 12 people out of 300 be selected for a jury?
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Question 87331: How many ways can 12 people out of 300 be selected for a jury?
Click here to see answer by Edwin McCravy(20054)

Question 87332: Please assist me with solving this.
Rosa's serves 11 appetizers, 26 main courses, 8 desserts, and 11 beverages. How many dinner combinations can be made if each includes one of each?
thanks!
Click here to see answer by favegirl13(22)

Question 87500: Thank you for any help you can give me.
If liscense plates are formed by 3 letters followed by 4 digits, how many different liscense plates can be made?
10 digits (0-9)
26 letters
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Question 87547: How may different 5-digit numbers that are odd and less than 50,000 can be formed using the digits 2,3,4,5,6,7 and 8 without repetition?
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Question 88720: in how many ways can you make a four-letter password from A, B, C, D, E if you are not allowed to repete characters?
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Question 88731: a club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold 2 offices, in how many ways can those offices be filled?
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035