A seven digit number is formed using digits 3,3,4,4,4,5,5.

Question

A seven digit number is formed using digits 3,3,4,4,4,5,5. Find the probability the number is divisible by 2.

Accepted Answer

Total arrangements $=\dfrac{7!}{3!2!2!}=210$. Divisible by 2 requires last digit 4: remaining digits 3,3,4,4,5,5 arranged in $\dfrac{6!}{2!2!2!}=90$ ways.

$$P = \frac{90}{210}=\frac37$$

Solutions · 1