If the number of 5-element subsets of the set | vedclass

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

Question

(C) The total number of $5$-element subsets of a set with $20$ elements is given by $^{20}C_5$.The number of $5$-element subsets containing a specific

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The total number of $5$-element subsets of a set with $20$ elements is given by $^{20}C_5$.The number of $5$-element subsets containing a specific element $a_4$ is equivalent to choosing $4$ more elements from the remaining $19$ elements,which is $^{19}C_4$.According to the problem,$^{20}C_5 = k 	imes ^{19}C_4$.Using the formula $^{n}C_r = \frac{n}{r} 	imes ^{n-1}C_{r-1}$,we have:$^{20}C_5 = \frac{20}{5} 	imes ^{19}C_4 = 4 	imes ^{19}C_4$.Comparing this with $k 	imes ^{19}C_4$,we get $k = 4$.

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ containing $20$ distinct elements is $k$ times the number of $5$-element subsets containing the element $a_4$,then what is the value of $k$?

Similar Questions

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then the range of $k$ is:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

The solution set of $^{10}C_{x-1} > 2 \cdot ^{10}C_x$ is

$A$ 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?

$A$ set contains $(2n + 1)$ elements. The number of subsets of the set which contain at most $n$ elements is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module