From a group of ^@8^@ men and ^@7^@ women, 5 persons are to be s | Math Question and Answer

Answer:

$546$

Step by Step Explanation:

We are required to select a $5$ -member committe from a group of $8$ men and $7$ women with at least $4$ men. This can be done in $2$ different ways:-
1. $4$ men and $1$ woman
2. $5$ men
Number of ways of selecting $4$ men and $1$ woman $= 8 C _4 \times 7 C _1$ $= \dfrac{ 8! }{ 4!(8 - 4)! } \times \dfrac{ 7! }{ 1!(7 - 1)! } = 490$
Number of ways of selecting $5$ men $= 8 C _5$ $= \dfrac{ 8! }{ 5!(8 - 5)! } = 56$
Now, required number of ways of selecting a $5$ -member committee $= 490 + 56 = 546$
Hence, there are $546$ ways of selecting a $5$ -member committee with at least $4$ men.

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