Please show work Seven orchids are to be selected from a col

Please show work.

Seven orchids are to be selected from a collection of 12 for a flower show. In how many ways can this be done? In how many different ways can the group of 7 be selected if 4 particular orchids must be included?

Solution

a)

seven orchids are to be selected from a collection of 12 is = 12 C 7 = 12! / (12-7)! * 7! = 792

b)

From the group 12 , 4 must be select in a selection, i.e. 4 C 4 & the reamaining slection to chosen are 3. We have left with 8 orchids now. Selction of 3 orchids from 8 will be = 4 C 4 * 8 C 3 = 1 * 56 = 56