# Find the differences between the largest values in the following: 14Cr and 12Cr - Mathematics and Statistics

Sum

Find the differences between the largest values in the following: ""^14"C"_r  "and"  ""^12"C"_r

#### Solution

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

""^14"C"_r  "and"  ""^12"C"_r

Maximum value of ""^14"C"_r  "occurs at"  r = 14/2 = 7

∴ Maximum value of ""^14"C"_r = ""^14"C"_7

= (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)

= 3432

Maximum value of ""^12"C"_r  "occurs at"  r = 12/2 = 6

∴ Maximum value of ""^12"C"_r = ""^12"C"_6

= (12 xx 11 xx 10 xx 9 xx 8 xx 7)/(8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2)

= 924

∴ The difference between the maximum values of ""^14"C"_r  "and"  ""^12"C"_r

= 3432 – 924
= 2508.

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 9. (i) | Page 90