Deadly King and others, i have another doubt, CIE Nov 06 Q 6 part 2
why 6! X 7C3?
I can't really explain the workings from the marking scheme but I did it another way which was approved by my teacher.
First we find out the number of arrangements in which all the 9 persons can be arranged. This will be
(9! +(7! x 3!))9! => There are nine persons which can be arranged in any way.
(7! x 3!) => There are 6 men and 3 women. We'll be taking all the women to be standing beside each other. Hence they are taken as one possiblity only which makes 7!. The 3 women can then be arranged in any way 3!.
Then we need to find the number of arrangements in which two women are next to each other =>
3(8! x 2!)8! = > One woman is taken as one possiblity and the other two as another possiblity. In all there will be 8 possiblities, after adding the six men.
Number of arrangements : (9! +(7! x 3!)) - 3(8! x 2!) =
151200Hope you understand