Question

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference.

a) How many delegations are possible?

b) How many of these delegations have all men?

c) How many of these delegations have at least one woman?

Answer 1

a) 5765760

b) 60480

c) 5705280

Explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

`n=(16!)/((16-6)!)=16*15*14*13*12*11\\ n= 5765760`

b) How many of these delegations have all men?

`n_(men) = (9!)/((9-6)!)=9*8*7*6*5*4 \\n_(men) = 60480`

c) How many of these delegations have at least one woman?

`n_(women >0)=n-n_(men)\\n_(women >0) =5765760-60480\\n_(women >0) =5705280`