Consider a class of 5 girls and 7 boys. number of different teams consisting of 2 girls and 3 boys t

English

Gujarati

Hindi

6.Permutation and Combination

hard

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is

$500$

$200$

$300$

$350$

(JEE MAIN-2019)

Solution

Number of ways $=$ Total number of ways without restriction $-$ When two specific boys are in team without any restriction, total number of ways of forming team is $^7{C_3}{ \times ^5}{C_2} = 350$ If two specific boys $B_1,B_2$ are in same team then total number of ways of forming team equals to $^5{C_1}{ \times ^5}{C_2} = 50$ ways total ways $=350-50=300$ ways

Standard 11

Mathematics

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl ?

medium

The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is

easy

Let

$S _1=\{( i , j , k ): i , j , k \in\{1,2, \ldots, 10\}\}$

$S _2=\{( i , j ): 1 \leq i < j +2 \leq 10, i , j \in\{1,2, \ldots, 10\}\},$

$S _3=\{( i , j , k , l): 1 \leq i < j < k < l, i , j , k , l \in\{1,2, \ldots ., 10\}\}$

$S _4=\{( i , j , k , l): i , j , k$ and $l$ are distinct elements in $\{1,2, \ldots, 10\}\}$

and If the total number of elements in the set $S _t$ is $n _z, r =1,2,3,4$, then which of the following statements is (are) TRUE?

$(A)$ $n _1=1000$ $(B)$ $n _2=44$ $(C)$ $n _3=220$ $(D)$ $\frac{ n _4}{12}=420$

normal

(IIT-2021)

The total number of three-digit numbers, with one digit repeated exactly two times, is

medium

(JEE MAIN-2022)

In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$