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The number of values of r satisfying the equation ^{39}C_{3r -

Question

The number of values of $r$ satisfying the equation
$^{39} C_{3 r - 1} -^{39} C_{r^{2}} =^{39} C_{r^{2} - 1} -^{39} C_{3 r}$ is

1

2

3

4

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Evelyn Discussed

The number of values of

r

satisfying the equation

^{39} C_{3 r - 1} -^{39} C_{r^{2}} =^{39} C_{r^{2} - 1} -^{39} C_{3 r}

10 mins ago

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10 mins ago

Text solutionVerified

Given,

^{39} C_{3 r - 1} -^{39} C_{r^{2}} =^{39} C_{r^{2} - 1} -^{39} C_{3 r}

\Rightarrow^{39} C_{3 r - 1} +^{39} C_{3 r} =^{39} C_{r^{2} - 1} +^{39} C_{r^{2}}

\Rightarrow^{40} C_{3 r} =^{40} C_{r^{2}}

\Rightarrow r^{2} = 3 r

r^{2} = 40 - 3 r

\Rightarrow r = 0, 3

- 8, 5

Thus

3

and

5

are the values as the given equation is not defined by

r = 0

and

r = - 8

Hence, the number of values of

r

2

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Question Text	The number of values of $r$ satisfying the equation $^{39} C_{3 r - 1} -^{39} C_{r^{2}} =^{39} C_{r^{2} - 1} -^{39} C_{3 r}$ is
Answer Type	Text solution:1
Upvotes	150