Question 1182133
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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<br>
Correct<br>
In how many ways can 4 boys and 2 girls seat themselves in a row if<br>
(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.<br>
Not quite. There are only 5 places the girls can start at. So 4!*2!*5 = 240.<br>
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.<br>
(b) the 2 girls are not to seat to each other
I did 6! - 2!(6-2+1)! = 480<br>
Correct.<br>
(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)<br>
Correct.<br>
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)<br>
Correct.<br>
(d) repetition of digits is allowed
I did 5*5*5*5*5<br>
Not quite; I think you know why. (Look at your answer for (e))<br>