A group of students comprises 5 boys and n gi | vedclass

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

Question

(D) Total students = $5 + n$.We need to select $3$ students such that there is at least one boy and at least one girl.The possible cases are:Case $1$:

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) Total students = $5 + n$.We need to select $3$ students such that there is at least one boy and at least one girl.The possible cases are:Case $1$: $1$ boy and $2$ girls: $^5C_1 	imes ^nC_2 = 5 	imes \frac{n(n-1)}{2} = \frac{5n(n-1)}{2}$.Case $2$: $2$ boys and $1$ girl: $^5C_2 	imes ^nC_1 = 10 	imes n = 10n$.Sum of ways = $\frac{5n(n-1)}{2} + 10n = 1750$.Multiply by $2$: $5n(n-1) + 20n = 3500$.Divide by $5$: $n(n-1) + 4n = 700$.$n^2 - n + 4n = 700 \Rightarrow n^2 + 3n - 700 = 0$.Solving the quadratic equation: $(n + 28)(n - 25) = 0$.Since $n$ must be positive,$n = 25$.

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways,in which a team of $3$ students can be randomly selected from this group such that there is at least one boy and at least one girl in each team,is $1750$,then $n$ is equal to

Similar Questions

The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,is

How many numbers can be formed from the digits $1, 2, 3, 4$ when repetition is not allowed?

Three letters are chosen at random from the letters of the word $VARIABLE$ and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is

The total number of three-digit numbers,divisible by $3$,which can be formed using the digits $1, 3, 5, 8$,if repetition of digits is allowed,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module