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.

Answer 1

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step 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?

$n=\frac{16!}{(16-6)!}=16*15*14*13*12*11\\ n= 5765760$

b) How many of these delegations have all men?

$n_{men} = \frac{9!}{(9-6)!}=9*8*7*6*5*4 \\n_{men} = 60480$

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

$n_{women >0}=n-n_{men}\\n_{women >0} =5765760-60480\\n_{women >0} =5705280$