Question 1182133: Hello, I just need someone to confirm my answers for these questions (if I'm wrong someone please help and correct me thank you:
In one section of a math test paper, a student answers 3 out of 4 questions in that section. In How many ways can this section be answered if different orders in which the questions are answered count as different ways.
My answer is 4*3*2 = 24
In how many ways can 4 boys and 2 girls seat themselves in a row if
(a) the 2 girls are to seat next to each other
(b) the 2 girls are not to seat to each other
(c) the 2 girls are to be separated by 2 boys between them
for (a) I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.
for (b) I did 6! - 2!(6-2+1)! = 480
for (c) I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)
in how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if
(e) no repetition of digits is allowed
(d) repetition of digits is allowed
for (e) I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)
for (d) i did 5*5*5*5*5
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
In one section of a math test paper, a student answers 3 out of 4 questions in that section. In How many ways can this section be answered if different orders in which the questions are answered count as different ways.
My answer is 4*3*2 = 24
Correct
In how many ways can 4 boys and 2 girls seat themselves in a row if
(a) the 2 girls are to seat next to each other
I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.
Not quite. There are only 5 places the girls can start at. So 4!*2!*5 = 240.
Alternatively....
Treat the 2 girls as one unit; there are then 5 things to be arranged, and there are 2 different arrangements in one of those things: (5!)(2)=240. Same answer by a different method.
(b) the 2 girls are not to seat to each other
I did 6! - 2!(6-2+1)! = 480
Correct.
(c) the 2 girls are to be separated by 2 boys between them
I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)
Correct.
In how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if
(e) no repetition of digits is allowed
I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)
Correct.
(d) repetition of digits is allowed
I did 5*5*5*5*5
Not quite; I think you know why. (Look at your answer for (e))
Answer by ikleyn(52779)  (Show Source):
You can put this solution on YOUR website! .
Hello, I just need someone to confirm my answers for these questions (if I'm wrong someone please help and correct me thank you:
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FIND my answers INSIDE YOUR TEXT
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In one section of a math test paper, a student answers 3 out of 4 questions in that section.
In How many ways can this section be answered if different orders in which the questions are answered count as different ways.
My answer is 4*3*2 = 24 <<<---=== Correct !
In how many ways can 4 boys and 2 girls seat themselves in a row if
(a) the 2 girls are to seat next to each other
(b) the 2 girls are not to seat to each other
(c) the 2 girls are to be separated by 2 boys between them
for (a) I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.
The correct solution is THIS: we have 5 objects (4 boys and two glued girls, which we consider as one object)
There are 5! = 120 permutations; and the glued object can be in one of
the two states (Ann,Barb) or (Barb,Ann).
So the total number of arrangements is 120*2 = 240. ANSWER
for (b) I did 6! - 2!(6-2+1)! = 480
Your answer number is correct.
My standard logic for it is 6! - 240 = 720 - 240 = 480. (the number 240 comes from part (a) ).
for (c) I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)
Correct
in how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if
(e) no repetition of digits is allowed
(d) repetition of digits is allowed
for (e) I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)
Correct.
for (d) i did 5*5*5*5*5
Incorrect.
The correct counting is 4*5*5*5*5 (zero can not be leading digit !)
Happy learning (!)
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