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प्रश्न
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
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उत्तर
Use `""^"n""C"_r` has maximum value if,
(a) r = `"n"/2` when n is even
(b) r = `("n" - 1)/2 "or" ("n" + 1)/2` when n is odd
`""^15"C"_r "and" ""^11"C"_r`
Maximum value of `""^15"C"_r "occurs at" r = 14/2 = 7 "or r = 16/2` = 8
∴ Maximum value of `""^15"C"_r = ""^15"C"_7 = ""^15"C"_8`
= `(15 xx 14 xx 13 xx 12 xx 11 xx 10 xx 9)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 6435
Maximum value of `""^11"C"_r "occurs at" r = 10/2 = 5 "or" r = 12/2` = 6
∴ Maximum value of `""^11"C"_r = ""^11"C"_5 = ""^11"C"_6`
`""^11"C"_r = ""^11"C"_5 = (11 xx 10 xx 9 xx 8 xx 7)/(5 xx 4 xx 3 xx 2 xx 1)`
= 462
∴ The difference between the maximum values of `""^15"C"_r "and" ""^11"C"_r`
= 6435 – 462
= 5973.
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