The number of values in set of values of r for which $$23Cr+2$$⋅$$23Cr+1+23Cr+2$$≥$$25C15$$ is $$______$$.

$$23Cr+2$$⋅$$23Cr+1+23Cr+2=24Cr+1+24Cr+2=25Cr+2$$≥$$25C15Therefore$$, (r$$ $$+$$ $$2) can be $$10$$, $$11$$,$$12$$ ,$$13$$,$$14$$ and $$15$$.So there are $$6$$ elements.

Binomial theorem for positive integral Index

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Question

The number of values in set of values of r for which $^{23} C_{r} + 2 \cdot^{23} C_{r + 1} +^{23} C_{r + 2} \geq^{25} C_{15}$ is ______.

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Solution

$^{23} C_{r} + 2 \cdot^{23} C_{r + 1} +^{23} C_{r + 2} =^{24} C_{r + 1} +^{24} C_{r + 2} =^{25} C_{r + 2} \geq^{25} C_{15}$
Therefore, (r + 2) can be 10, 11,12 ,13,14 and 15.
So there are 6 elements.

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