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प्रश्न
Find the differences between the greatest values in the following:
13Cr and 8Cr
उत्तर
The greatest value of nCr occurs at r = `"n"/2`, if n is even and at r = `("n" - 1)/2`, if n is odd.
The greatest value of 13Cr occurs at
r = `(13 - 1)/2` = 6 ...[∵ n = 13 is odd]
∴ the greatest value of 13Cr
= 13C6
= `(13!)/(6!7!)`
= `(13 xx 12 xx 11 xx 10 xx 9 xx 8)/(6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 13 × 11 × 2 × 3 × 2
= 1716
The greatest value of 8Cr occurs at
r = `8/2` = 4 ...[∵ n = 8 is even]
∴ the greatest value of 8Cr
= 8C4
= `(8!)/(4!4!)`
= `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1)`
= 7 × 2 × 5
= 70
∴ the difference between the greatest values of 13Cr and 8Cr
= 1716 – 70
= 1646
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