A man has 7 relatives,4 of them are ladies an | vedclass

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

Question

(C) Let $m_L, m_G$ be the number of ladies and gents invited from the man's relatives,and $w_L, w_G$ be the number of ladies and gents invited from th

Vedclass · Accepted Answer

$485$

Vedclass · Answer

(C) Let $m_L, m_G$ be the number of ladies and gents invited from the man's relatives,and $w_L, w_G$ be the number of ladies and gents invited from the wife's relatives.We need $m_L + w_L = 3$ and $m_G + w_G = 3$,where $0 \le m_L, m_G \le 3$ and $0 \le w_L, w_G \le 3$.The man has $4$ ladies and $3$ gents. The wife has $3$ ladies and $4$ gents.The possible cases for $(m_L, m_G)$ and $(w_L, w_G)$ are:$1$. $(m_L, m_G) = (0, 3)$ and $(w_L, w_G) = (3, 0)$: Ways $= {^4C_0} 	imes {^3C_3} 	imes {^3C_3} 	imes {^4C_0} = 1 	imes 1 	imes 1 	imes 1 = 1$.$2$. $(m_L, m_G) = (1, 2)$ and $(w_L, w_G) = (2, 1)$: Ways $= {^4C_1} 	imes {^3C_2} 	imes {^3C_2} 	imes {^4C_1} = 4 	imes 3 	imes 3 	imes 4 = 144$.$3$. $(m_L, m_G) = (2, 1)$ and $(w_L, w_G) = (1, 2)$: Ways $= {^4C_2} 	imes {^3C_1} 	imes {^3C_1} 	imes {^4C_2} = 6 	imes 3 	imes 3 	imes 6 = 324$.$4$. $(m_L, m_G) = (3, 0)$ and $(w_L, w_G) = (0, 3)$: Ways $= {^4C_3} 	imes {^3C_0} 	imes {^3C_0} 	imes {^4C_3} = 4 	imes 1 	imes 1 	imes 4 = 16$.Total ways $= 1 + 144 + 324 + 16 = 485$.

$A$ man has $7$ relatives,$4$ of them are ladies and $3$ are gents; his wife has $7$ other relatives,$3$ of them are ladies and $4$ are gents. The number of ways they can invite $3$ ladies and $3$ gents to a party such that there are $3$ of the man's relatives and $3$ of the wife's relatives,is:

Similar Questions

The number of integers lying between $1000$ and $10000$ such that the sum of all the digits in each of those numbers becomes $30$ is:

The sum of all possible numbers that can be formed by using the digits $2, 3, 5, 7$ without repetition of digits is

The last two digits of $2015! + 3^{2015}$ are:

How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 4,$ and $5$ without repetition such that the number is divisible by $3$?

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module