If set A-r-s - r-s- r-s- then the number of elements in set A such that 7Cr- 7Cr-1- 8Cs is

Given : nbsp;^7C_r+ ^7C_r 1= ^8C_s nbsp; ⇒ ^8C_r= ^8C_s (∵ ^nC_r+ ^nC_r 1= ^n+1C_r) ⇒ r+s=8 or r=s but r lt;s also r 1≥0 ⇒ r≥1 ∴ Possible pairs of (r,s): ...

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Standard XI

Mathematics

Permutations and Combinations

If set A=r,s ...

Question

If set $A = {(r, s) | r < s; r, s \in W}$ , then the number of elements in set $A$ such that $^{7} C_{r} +^{7} C_{r - 1} =^{8} C_{s}$ is

8

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Solution

The correct option is D $3$
Given : $^{7} C_{r} +^{7} C_{r - 1} =^{8} C_{s}$
$\Rightarrow^{8} C_{r} =^{8} C_{s}$
$(∵^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r})$

$\Rightarrow r + s = 8$ or $r = s$ but $r < s$
also $r - 1 \geq 0 \Rightarrow r \geq 1$
$∴$ Possible pairs of $(r, s) :$ $(1, 7), (2, 6), (3, 5)$
$∴$ Number of elements in set $A = 3$

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Permutations and Combinations

Standard XI Mathematics

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If set A={(r,s) | r<s; r,s∈W}, then the number of elements in set A such that 7Cr+ 7Cr−1= 8Cs is

The correct option is D 3Given : 7Cr+ 7Cr−1= 8Cs ⇒ 8Cr= 8Cs (∵ nCr+ nCr−1= n+1Cr) ⇒ r+s=8 or r=s but r<s also r−1≥0 ⇒ r≥1 ∴ Possible pairs of (r,s): (1,7),(2,6),(3,5) ∴ Number of elements in set A=3

If set $A = {(r, s) | r < s; r, s \in W}$ , then the number of elements in set $A$ such that $^{7} C_{r} +^{7} C_{r - 1} =^{8} C_{s}$ is