The least value of natural number n satisfyin | vedclass

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

Question

(A) Using the Pascal's identity,$^nC_r + ^nC_{r-1} = ^{n+1}C_r$,we have $^nC_6 + ^nC_5 = ^{n+1}C_6$.Given the inequality: $^{n+1}C_6 > ^{n+1}C_5$.Expa

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(A) Using the Pascal's identity,$^nC_r + ^nC_{r-1} = ^{n+1}C_r$,we have $^nC_6 + ^nC_5 = ^{n+1}C_6$.Given the inequality: $^{n+1}C_6 > ^{n+1}C_5$.Expanding the combinations: $\frac{(n+1)!}{6!(n-5)!} > \frac{(n+1)!}{5!(n-4)!}$.Dividing both sides by $(n+1)!$ and simplifying the factorials:$\frac{1}{6 	imes 5!(n-5)!} > \frac{1}{5!(n-4)(n-5)!}$.$\frac{1}{6} > \frac{1}{n-4}$.Since $n$ is a natural number,$n-4 > 6$,which implies $n > 10$.The least natural number $n$ satisfying this condition is $11$.

The least value of natural number $n$ satisfying $C(n, 5) + C(n, 6) > C(n + 1, 5)$ is

Similar Questions

There are $6$ items in column $A$ and $6$ items in column $B$. $A$ student is asked to match each item in column $A$ with an item in column $B$. How many possible (correct or incorrect) answers are there to this question?

In how many different ways can the letters of the word '$DETAIL$' be arranged in such a way that the vowels occupy only the odd positions?

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

If $^{12}P_r = 1320$,then $r$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module