If { }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ } | vedclass

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

Question

(C) We use the Pascal's identity: ${ }^{n} C_{r}+{ }^{n} C_{r-1}={ }^{n+1} C_{r}$.Given expression: ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) We use the Pascal's identity: ${ }^{n} C_{r}+{ }^{n} C_{r-1}={ }^{n+1} C_{r}$.Given expression: ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$.Applying the identity to the first two terms: ${ }^{11} C_4+{ }^{11} C_5 = { }^{12} C_5$.Now the expression becomes: ${ }^{12} C_5+{ }^{12} C_6+{ }^{13} C_7$.Applying the identity again: ${ }^{12} C_5+{ }^{12} C_6 = { }^{13} C_6$.Now the expression becomes: ${ }^{13} C_6+{ }^{13} C_7$.Applying the identity one last time: ${ }^{13} C_6+{ }^{13} C_7 = { }^{14} C_7$.Comparing this with ${ }^{14} C_{r}$,we get $r = 7$.

If ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$,then the value of $r$ is

Similar Questions

In how many ways can we select any $4$ letters from the word $CORGOO$?

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

In how many ways can $10$ people be seated in $2$ boats such that each boat has $5$ people and two specific people do not sit in the same boat?

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?

In how many ways can a committee of $6$ members be formed from $8$ men and $4$ women such that the committee contains at least $3$ women?

Vedclass Test Series

Exam Paper Generator

Online Exam Module