# SOLUTION: I just need someone to kindly look over these problems and let me know if I did them correctly. 1. In how many ways can three drivers be hired from a pool of 10 applicants to dr

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 Click here to see ALL problems on Probability-and-statistics Question 462120: I just need someone to kindly look over these problems and let me know if I did them correctly. 1. In how many ways can three drivers be hired from a pool of 10 applicants to drive three identical cars? 3!10? 2. In how many ways can three drivers be hired from a pool of 10 applicants to drive a sedan, a minivan, and a pickup truck? 3!10 x 3!? 3. A coin is flipped 12 times and the sequence of heads and tails is observed. In how many ways can the sequence consist of exactly 7 heads and 5 tails? I dont know how to set this one up! 5. In how many ways can 2 C’s, 4 D’s, and 6 F’s be awarded to 12 politicians, one letter for each politician? 2!4!6!12!? 6. 15 people enter an art contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected? 15!3 7. In how many different ways can a committee of 9 members be chosen from 6 freshmen, 5 sophomores, and 4 juniors if the committee must consist of 4 freshmen, 3 sophomores, and 2 juniors? 9!6!5!4! x 4!3!2! 8.In how many different ways can a committee of 9 members be chosen from 6 freshmen, 5 sophomores, and 4 juniors if the committee must consist of at least one freshman? 9!6!5!4! x 6! .Answer by stanbon(57984)   (Show Source): You can put this solution on YOUR website!I just need someone to kindly look over these problems and let me know if I did them correctly. 1. In how many ways can three drivers be hired from a pool of 10 applicants to drive three identical cars? Ans: 10C3 = (10*9*8)/(1*2*3) = 120 ways because you are counting groups of 3. -------------------------------------------------- 2. In how many ways can three drivers be hired from a pool of 10 applicants to drive a sedan, a minivan, and a pickup truck? Ans: 10P3 = 10*9*8 = 720 ways because order is implied. ----------------------------------- 3. A coin is flipped 12 times and the sequence of heads and tails is observed. In how many ways can the sequence consist of exactly 7 heads and 5 tails? ------ Ans: 12C5 = (12*11*10*9*8)/(1*2*3*4*5) = 792 ----------------------------------------------------- 5. In how many ways can 2 C’s, 4 D’s, and 6 F’s be awarded to 12 politicians, one letter for each politician? Ans: 12!/(2!*4!*6!) = 13,860 ways Similar to # of 12-letter words with 2C's, 4D's, and 6F's. -------------------------------------- 6. 15 people enter an art contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected? Ans: Order is implied: 15P3 = 15*14*13 = 2730 ways ----------------------------------------------------- 7. In how many different ways can a committee of 9 members be chosen from 6 freshmen, 5 sophomores, and 4 juniors if the committee must consist of 4 freshmen, 3 sophomores, and 2 juniors? Ans: 6C4*5C3*4C2 = 15*10*6 = 900 ways ------------------------------------------------ 8.In how many different ways can a committee of 9 members be chosen from 6 freshmen, 5 sophomores, and 4 juniors if the committee must consist of at least one freshman? Ans: #'s in the order of (frosh;soph;juniors) The limits are 6 frosh;5 soph;4 juniors =============================================== 1:5;3 (this means 1 frosh; 5 soph; 3 juniors): # of ways = 6*5*4C3 = 6*5*4 = 120 1;4;4::: # of ways = 6*5C4*4C4 = 30 -------- I'll leave the rest for you to figure out. =================== 2;4;3 2;3;4 ------- 3:4;2 3:3:3 3;2:4 ---------- 4:4:1 4;3;2 4;2;3 4;1;4 -------- 5;4;0 5;3;1 5;2;2 5;1;3 5;0;4 ------- 6;3;0 6;2;1 6;1;2 6;0;3 ============== Cheers, Stan H. ================