If 15 C 3 r -15 C r -3- then the value of r is -A- 3B- 4C- 5D- 8

The correct option is A 3 ^15C_3r=^15C_r+3 If we consider 3r=r+3 r=3 2, BUT r cannot be a fraction So,use the property ^nC_r=^nC_n+3 ^15C_15 3r=^15C_r+3 Then, ...

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Byju's Answer

Standard XII

Mathematics

Finding Integral Part of Numbers of the Form a^b Where a Is Irrational

If 15 C 3 r =...

Question

If $^{15} C_{3 r} =^{15} C_{r + 3}$ , then the value of r is ........

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Solution

The correct option is A
3

$^{15} C_{3 r} =^{15} C_{r + 3}$
If we consider 3r=r+3
$r = \frac{3}{2}$ , BUT r cannot be a fraction
So,use the property
$^{n} C_{r} =^{n} C_{n + 3}$
$^{15} C_{15 - 3 r} =^{15} C_{r + 3}$
Then,
$15 - 3 r = r + 3$
$4 r = 12$
$r = 3$

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If 15C3r=15Cr+3, then the value of r is ........

The correct option is A 3 15C3r=15Cr+3 If we consider 3r=r+3 r=32, BUT r cannot be a fraction So,use the property nCr=nCn+3 15C15−3r=15Cr+3 Then, 15−3r=r+3 4r=12 r=3

If $^{15} C_{3 r} =^{15} C_{r + 3}$ , then the value of r is ........

The correct option is A
3

$^{15} C_{3 r} =^{15} C_{r + 3}$
If we consider 3r=r+3
$r = \frac{3}{2}$ , BUT r cannot be a fraction
So,use the property
$^{n} C_{r} =^{n} C_{n + 3}$
$^{15} C_{15 - 3 r} =^{15} C_{r + 3}$
Then,
$15 - 3 r = r + 3$
$4 r = 12$
$r = 3$