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प्रश्न
Find the differences between the greatest values in the following:
15Cr and 11Cr
उत्तर
Greatest value of 15Cr
Here n = 15, which is odd
Greatest value of nCr occurs at r = `("n" - 1)/2` if n is odd
∴ r = `("n" - 1)/2`
∴ r = `(15 - 1)/2` = 7
∴ Greatest value of 15Cr
= 15C7
= `(15!)/(7!8!)`
= `(15 xx 14 xx 13 xx 12 xx 11 xx 10 xx 9 xx 8!)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1 xx 8!)`
= 6435
Also, for greatest value of 11Cr
n = 11, which is odd
∴ r = `(11 - 1)/2` = 5
∴ 11C5 = `(11!)/(5!6!)`
= `(11 xx 10 xx 9 xx 8 xx 7 xx 6!)/(5 xx 4 xx 3 xx 2 xx 1 xx 6!)`
= 462
∴ Difference between the greatest values of 15Cr and 11Cr
= 15Cr – 11Cr
= 6435 – 462
= 5973
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