If x,y,z are integers and x ≥ 0 , y ≥ 1, z ≥ 2 and x + y +

1.	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» 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

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»

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