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If nCr : nCr+1 = 1 : 2 and nCr+1 : nCr+2 = 2 : 3 determine the values of n and r.

(a) n = 10, r = 6 

(b) n = 12, r = 6 

(c) n = 10, r = 4 

(d) n = 14, r = 4

1 Answer

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Best answer

(d) n = 14, r = 4

nCr : nCr+1 = 1 : 2 and nCr+1 : nCr+2 = 2 : 3

⇒ 2r + 2 = n – r and 3r + 6 = 2n – 2r – 2 

⇒ n – 3r = 2 and 2n – 5r = 8 

Solving the two simultaneous equations, we get n = 14, r = 4.

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