Question

Find the difference between the greatest values of
(a) $\rm ^{13}C_{r}-\ ^{11}C_{r}$
(b) $\rm ^{14}C_{r}-\ ^{8}C_{r}$
(c) $\rm ^{15}C_{r}-\ ^{12}C_{r}$

Answer 1

Answer:

(a) 1254

(b) 3362

(c) 5511

Step-by-step explanation:

Hi,

Greatest value of ⁿCₓ occurs at x = n/2 if n is even

at x = (n-1)/2 or (n + 1)/2, if n is odd

(a)

Greatest value of ¹³Cr is ¹³C₆ = 13*12*11*10*9*8/6! = 1716

Greatest value of ¹¹Cr is ¹¹C₅ = 11*10*9*8*7/5! = 462

Hence, the difference is 1716 - 462 = 1254

(b)

Greatest value of ¹⁴Cr is ¹⁴C₇ = 14*13*12*11*10*9*8/7! = 3432

Greatest value of ⁸Cr is ⁸C₄ = 8*7*6*5/4! = 70

Hence, the difference is 3432 - 70 = 3362

(c)

Greatest value of ¹⁵Cr is ¹⁵C₇ = 15*14*13*12*11*10*9/7! = 6435

Greatest value of ¹²Cr is ¹²C₆ = 12*11*10*9*8*7/6! = 924

Hence, the difference is 6435 - 924 = 5511

Hope, it helps !