If n C 2- n C 3- n -1 C r- then the minimum possible value of r isA- 0B- 3C- 2D- 1

The correct option is D 1Given ^nC_2+ ^nC_3 = ^n+1C_r We know that, nbsp; ^nC_r+ ^nC_r 1 = ^n+1C_r So, ^nC_2+ ^nC_3 = ^n+1C_r ⇒ nbsp; ^n+1C_3 = nbsp; ...

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Standard XII

Mathematics

Pascal Triangle

If n C 2+ n C...

Question

If $^{n} C_{2} +^{n} C_{3} =^{n + 1} C_{r}$ , then the minimum possible value of $r$ is

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Solution

The correct option is D $1$
Given $^{n} C_{2} +^{n} C_{3} =^{n + 1} C_{r}$
We know that,
$^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$
So,
$^{n} C_{2} +^{n} C_{3} =^{n + 1} C_{r} \Rightarrow^{n + 1} C_{3} =^{n + 1} C_{r} \Rightarrow r = 3 or r + 3 = n + 1 ∴ r = 3, n - 2$
From the given expression we know that,
$n \geq 3$
So, the minimum possible value of $r$ is $1$ when $n = 3.$

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If nC2+ nC3= n+1Cr, then the minimum possible value of r is

The correct option is D 1Given nC2+ nC3= n+1Cr We know that, nCr+ nCr−1= n+1Cr So, nC2+ nC3= n+1Cr⇒ n+1C3= n+1Cr⇒r=3 or r+3=n+1∴r=3,n−2 From the given expression we know that, n≥3 So, the minimum possible value of r is 1 when n=3.

If $^{n} C_{2} +^{n} C_{3} =^{n + 1} C_{r}$ , then the minimum possible value of $r$ is