calculate the number of possible outcomes for the following

Calculate the number of possible outcomes for the following experiments. 10a 4 items are selected from a group of 15. Order does NOT matter. 10b 9 items are selected from a group of 15 Order matters.

Solution

10 a) 4 items can be selected from a group of 15 items in ¹⁵C₄ ways

= 15! / (4! * 11!) = 15* 14* 13* 12 *11! / (4*3*2*11!)

= 15* 7*13 = 1365 ways

So there are 1365 ways in which 4 items can be selected from a group of 15 items

10 b) 9 items can be selected from group of 15 items when order matters in ¹⁵P₉ ways

= 15!/9! = 15*14*13*12*11*10 = 3603600 ways

So there are 3603600 ways in which 9 items can be selected from a group of 15 items when order matters