The value of 15 C8-15 C9-15 C6-15 C7 is

15C8 + 15C9 minus; 15C6 nbsp; minus; 15C7 nbsp; Since nCr = nCn minus; r nbsp; rArr; 15C6 = 15C15 minus;6 = 15C9 nbsp; nbsp; nbsp; ... ...

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Byju's Answer

Standard VI

Mathematics

Operations on Number Line

The value of ...

Question

The value of ¹⁵C₈ = ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ is ___________.

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Solution

¹⁵C₈ + ¹⁵C₉ − ¹⁵C₆− ¹⁵C₇
Since ⁿC_r = ⁿC_{n − r}
⇒ ¹⁵C₆ = ¹⁵C₁₅₋₆ = ¹⁵C₉ ...(1)
and ¹⁵C₇ = ¹⁵C₁₅₋₇ = ¹⁵C₈ ...(2)
∴¹⁵C₈ + ¹⁵C₉ − ¹⁵C₉ −¹⁵C₈ = 0 (∵ from (1) and (2))

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