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प्रश्न
Find the differences between the greatest values in the following:
14Cr and 12Cr
उत्तर
Greatest value of 14Cr
Here n = 14, which is even
Greatest value of nCr occurs at r = `"n"/2` if n is even
∴ r = `"n"/2`
∴ r = `14/2` = 7
∴ Greatest value of 14Cr = 14C7 = `(14!)/(7!7!)`
= `(14 xx 13 xx 12 xx 11 xx 10 xx 9 xx 8 xx 7!)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1 xx 7!)`
= 3432
Also, for greatest value of 12Cr
n = 12, which is even
∴ r = `12/2` = 6
∴ 12C6 = `(12!)/(6!6!)`
= `(12 xx 11 xx 10 xx 9 xx 8 xx 7 xx 6!)/(6 xx 5 xx 4 xx 3 xx 2 xx 1 xx 6!)`
= 924
∴ Difference between the greatest values of 14Cr and 12Cr
= 14Cr and 12Cr
= 3432 – 924
= 2508
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