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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 :

pedrocarratore

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?

[tex]n=\frac{16!}{(16-6)!}=16*15*14*13*12*11\\ n= 5765760[/tex]

b) How many of these delegations have all men?

[tex]n_{men} = \frac{9!}{(9-6)!}=9*8*7*6*5*4 \\n_{men} = 60480[/tex]

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

[tex]n_{women >0}=n-n_{men}\\n_{women >0} =5765760-60480\\n_{women >0} =5705280[/tex]

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