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Find the differences between the greatest values in the following: 15Cr and 11Cr - Mathematics and Statistics

Sum

Find the differences between the greatest values in the following:

15Cr and 11Cr 

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Solution

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 11C

= 15Cr11Cr

= 6435 – 462

= 5973

  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.6 | Q 20. (c) | Page 65
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