Acertain law firm consists of 4 senior partners and 6 junior partners.
how many different groups of 3 partners can be formed in which at least one member of the group is a senior partner?

a) 48 b) 100 c) 120 d) 288 e) 600

b) 100

Step-by-step explanation:

Given : Number of senior partners  =4

Number of  junior partners. = 6

Total partners = 4+ 6= 10

Total Number of ways to choose 3 partners

i.e. Total Number of ways to choose 3 partners =120

The number of ways that none of 3 partners are seniors =tex]=^{6}C_3=\dfrac{6!}{3!(6-3)!}=20[/tex]

Now , the different groups of 3 partners can be formed in which at least one member of the group is a senior partner

= Total Number of ways to choose 3 partners- Number of ways that none of 3 partners are seniors

= 120-20=100

Hence, the correct answer is b) 100.

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