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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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:

Similar Questions

$A$ bag contains $23$ balls, of which $7$ are identical. The number of ways of selecting $12$ balls from the bag is:

If $\binom{189}{35} + \binom{189}{x} = \binom{190}{x}$,then $x = \dots$

Let $n$ and $k$ be positive integers such that $n \ge \frac{k(k + 1)}{2}$. The number of solutions $(x_1, x_2, ..., x_k)$ where $x_1 \ge 1, x_2 \ge 2, ..., x_k \ge k$ are all integers,satisfying $x_1 + x_2 + ... + x_k = n$,is

In how many ways can $12$ balls be distributed between two friends such that one gets $8$ balls and the other gets $4$ balls?

Two players $A$ and $B$ play a series of games of badminton. The player, who wins $5$ games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player $A$ wins the series is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module