A committee of 4 persons is to be formed from | vedclass

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(B) We need to select $4$ persons from $2$ ladies $(L)$,$2$ old men $(O)$,and $4$ young men $(Y)$ with the constraints: $L \ge 1$,$O \ge 1$,and $Y \le

Vedclass · Accepted Answer

$41$

Vedclass · Answer

(B) We need to select $4$ persons from $2$ ladies $(L)$,$2$ old men $(O)$,and $4$ young men $(Y)$ with the constraints: $L \ge 1$,$O \ge 1$,and $Y \le 2$.The possible combinations $(L, O, Y)$ that sum to $4$ are:$1. (1, 1, 2) \implies ^2C_1 	imes ^2C_1 	imes ^4C_2 = 2 	imes 2 	imes 6 = 24$$2. (1, 2, 1) \implies ^2C_1 	imes ^2C_2 	imes ^4C_1 = 2 	imes 1 	imes 4 = 8$$3. (2, 1, 1) \implies ^2C_2 	imes ^2C_1 	imes ^4C_1 = 1 	imes 2 	imes 4 = 8$$4. (2, 2, 0) \implies ^2C_2 	imes ^2C_2 	imes ^4C_0 = 1 	imes 1 	imes 1 = 1$Total number of ways $= 24 + 8 + 8 + 1 = 41$.

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

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