First slide

Combinations

Question

The positive integer r, such that _{$^{15} C_{3 r} =^{15} C_{r + 3}$} is equal to

Easy

A

3
B

4
C

5
D

2

Solution

$^{15} c_{3 r} =^{15} c_{r + 3}$
$\Rightarrow 3 r = r + 3 o r 3 r + r + 3 = 15$ $(I f c (n, r) = c (n, s) t h e n e i t h e r r = s o r r + s = n)$
$\Rightarrow 2 r = 3 \Rightarrow 4 r = 12$
$\Rightarrow r = \frac{3}{2} \Rightarrow r = 3$
$r = \frac{3}{2} i s n o t p o s s i b l e$ $\sin c e r i s n o n n e g a t i v e i n t e g e r$
$\Rightarrow r = 3$

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