JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Probability

A seven digit number is formed using digits

3, 3, 4, 4, 4, 5, 5

. The probability, that number so formed is divisible by 2 , is :

Answer: (A)

Solution

The seven digits

3, 3, 4, 4, 4, 5, 5

form

\frac{7 !}{2 ! 3 ! 2 !} = 210

distinct numbers, all equally likely. Such a number is divisible by

2

exactly when its last digit is even, and the only even digit available is

4

. Placing a

4

in the units place leaves

3, 3, 4, 4, 5, 5

for the other six places, which can be ordered in

\frac{6 !}{2 ! 2 ! 2 !} = 90

ways. The required probability is

\frac{90}{210} = \frac{3}{7}

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Single correct option