Three randomly chosen non-negative integers x, y and z are… — JEE Main 2017 Mathematics PYQ

JEE Main 2017

Three randomly chosen non-negative integers

x

y

and

z

are found to satisfy the equation

x + y + z = 10

. Then the probability that

z

is even, is

A.
$\frac{1}{2}$
B.
$\frac{36}{55}$
C.
$\frac{6}{11}$
D.
$\frac{5}{11}$

Show answer and solution

Correct option: C

Solution

Total solutions of x+y+z=10 in non-negative integers = C(12,2) = 66.

For z even, let z = 2k where k = 0,1,2,3,4,5. For each value of z=2k, the number of solutions for x+y=10-2k is (10-2k+1) = 11-2k.

Summing over k=0 to 5: (11+9+7+5+3+1) = 36.

Probability = 36/66 = 6/11.

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