Question

If x,y,z are integers and x ≥ 0 , y ≥ 1, z ≥ 2 and x + y + z = 15, then the number of ordered triplets (x,y,z) is 

(a)  91 

(b)  455 

(c)  17C₂ 

(d)  none of these

Answer 1

Correct option (a)  91

Explanation:

x ≥ 0, y ≥ 1, z ≥ 2 and x + y + z = 15

we can say 12 objects (alike) are to be distributed among 3 persons. (distribution of alike objects)

Apply ^n+r–1C_r–1 when n = 12, r = 3

^12+3–1C_3–1 = ¹⁴C₂ = 2 14 x 13/2 = 91