If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$; then the probability that their sum as well as absolute difference are both multiple of 4, is :

JEE Main · 2017 · 02 Apr 2017 · Offline · Probability

If two different numbers are taken from the set

{0, 1, 2, 3, \dots\dots, 10}

; then the probability that their sum as well as absolute difference are both multiple of 4, is :

Answer: (B)

There are

(2 11) = 55

ways to choose two numbers. For both the sum and the difference to be multiples of

4

, the two must share residue mod

4

(that handles the difference) and that residue must be

0

2

(that handles the sum). From

{0, 4, 8}

this gives

(2 3) = 3

pairs and from

{2, 6, 10}

another

3

, so

6

favourable pairs in all. The probability is

\frac{6}{55}

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option