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

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

Question

(B) Let $P$ invite $l_1$ ladies and $m_1$ men from his friends,and $Q$ invite $l_2$ ladies and $m_2$ men from her friends.Given that $P$ invites $3$ f

Vedclass · Accepted Answer

$485$

Vedclass · Answer

(B) Let $P$ invite $l_1$ ladies and $m_1$ men from his friends,and $Q$ invite $l_2$ ladies and $m_2$ men from her friends.Given that $P$ invites $3$ friends,so $l_1 + m_1 = 3$.Given that $Q$ invites $3$ friends,so $l_2 + m_2 = 3$.The total number of ladies invited is $l_1 + l_2 = 3$.The total number of men invited is $m_1 + m_2 = 3$.We have the following cases:Case $1$: $l_1=3, m_1=0$ and $l_2=0, m_2=3$. Number of ways = $^4C_3 	imes ^3C_0 	imes ^3C_0 	imes ^4C_3 = 4 	imes 1 	imes 1 	imes 4 = 16$.Case $2$: $l_1=2, m_1=1$ and $l_2=1, m_2=2$. Number of ways = $^4C_2 	imes ^3C_1 	imes ^3C_1 	imes ^4C_2 = 6 	imes 3 	imes 3 	imes 6 = 324$.Case $3$: $l_1=1, m_1=2$ and $l_2=2, m_2=1$. Number of ways = $^4C_1 	imes ^3C_2 	imes ^3C_2 	imes ^4C_1 = 4 	imes 3 	imes 3 	imes 4 = 144$.Case $4$: $l_1=0, m_1=3$ and $l_2=3, m_2=0$. Number of ways = $^4C_0 	imes ^3C_3 	imes ^3C_3 	imes ^4C_0 = 1 	imes 1 	imes 1 	imes 1 = 1$.Total number of ways = $16 + 324 + 144 + 1 = 485$.

Similar Questions

$A$ five-digit number divisible by $3$ is to be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition. The total number of ways this can be done is:

The number of permutations of the letters $a_1, a_2, a_3, a_4, a_5$ in which the first letter $a_1$ does not occupy the first position and the second letter $a_2$ does not occupy the second position is:

The number of ways to distribute $30$ identical candies among four children $C_{1}, C_{2}, C_{3}$ and $C_{4}$ such that $C_{2}$ receives at least $4$ and at most $7$ candies,and $C_{3}$ receives at least $2$ and at most $6$ candies,is equal to

The number of integers $n$ such that $100 \leq n \leq 999$ and $n$ contains at most two distinct digits is:

The number of all $3$-digit numbers $abc$ (in base $10$) for which $(a \times b \times c) + (a \times b) + (b \times c) + (c \times a) + a + b + c = 29$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module