(B) The expression is $\sum_{r=1}^{5} C(5, r) = C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4) + C(5, 5)$.We know that the sum of binomial coefficients is $\su

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

(B) The expression is $\sum_{r=1}^{5} C(5, r) = C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4) + C(5, 5)$.We know that the sum of binomial coefficients is $\sum_{r=0}^{n} C(n, r) = 2^n$.Here,$n = 5$,so $\sum_{r=0}^{5} C(5, r) = 2^5 = 32$.The given sum is $\sum_{r=1}^{5} C(5, r) = \left( \sum_{r=0}^{5} C(5, r) \right) - C(5, 0)$.Since $C(5, 0) = 1$,we have $32 - 1 = 31$.Thus,the correct option is $B$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Medium

Find $\sum_{r=1}^{5} C(5, r)$

A
$41$
B
$31$
C
$51$
D
$61$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Permutation and Combination

Subtopic

Permutation and Combination

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

Difficult

View Solution

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,is

Difficult

View Solution

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is

Difficult

View Solution

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

Difficult

View Solution

There are seven candidates for $3$ posts. In how many ways can the posts be filled?

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Find $\sum_{r=1}^{5} C(5, r)$

Similar Questions

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,is

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

There are seven candidates for $3$ posts. In how many ways can the posts be filled?

Vedclass Test Series

Exam Paper Generator

Online Exam Module