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If x,y,z is integer and xge0,yge1,zge2,...

If x,y,z is integer and `xge0,yge1,zge2,x+y+z=15` then the number of values of the ordered triplet (x,y,z) is

A

91

B

455

C

`""^(17)C_(15)`

D

none of these

Text Solution

Verified by Experts

Let `y'=y-1andz'=z-2`. Then,
x+y+z=15
`impliesx+y'+z'=12` where `xge0,y'ge0andz'ge0`
The total number of solutions of this equations is
`""^(12+3-1)C_(3-1)=""^(14)C_(2)`
Hence, required number of ordered triplets (x, y, z) is
`""^(14)C_(2)=91`.
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