Let S = {1, 2, 3, ldots, 9}. For k = 1, 2, ld | vedclass

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

Question

(D) The set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ contains $5$ odd numbers $\{1, 3, 5, 7, 9\}$ and $4$ even numbers $\{2, 4, 6, 8\}$.We are looking for

Vedclass · Accepted Answer

$126$

Vedclass · Answer

(D) The set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ contains $5$ odd numbers $\{1, 3, 5, 7, 9\}$ and $4$ even numbers $\{2, 4, 6, 8\}$.We are looking for the total number of subsets of $S$ with $5$ elements,where the number of odd elements $k$ can be $1, 2, 3, 4,$ or $5$.Since there are only $4$ even numbers in $S$,any subset of $5$ elements must contain at least $5 - 4 = 1$ odd number.Therefore,the sum $N_1 + N_2 + N_3 + N_4 + N_5$ represents the total number of ways to choose $5$ elements from the $9$ elements in $S$.This is given by the combination formula $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.$N_1 + N_2 + N_3 + N_4 + N_5 = \binom{9}{5} = \binom{9}{4} = \frac{9 	imes 8 	imes 7 	imes 6}{4 	imes 3 	imes 2 	imes 1} = 126$.

Let $S = \{1, 2, 3, \ldots, 9\}$. For $k = 1, 2, \ldots, 5$,let $N_k$ be the number of subsets of $S$,each containing five elements out of which exactly $k$ are odd. Then $N_1 + N_2 + N_3 + N_4 + N_5 =$

Similar Questions

The value of $\sum_{r=0}^4 {}^{(19-r)} C_3 + {}^{15} C_4$ is equal to

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels?

Everybody in a room shakes hands with everybody else. The total number of handshakes is $45$. The total number of persons in the room is

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

In how many ways can a team of $11$ players be formed out of $25$ players,if $6$ out of them are always to be included and $5$ are always to be excluded?

Vedclass Test Series

Exam Paper Generator

Online Exam Module