Of all the five digit numbers that can be formed with the digits $0, 1, 3, 5, 7$ and $9$ without repetition of the digit, a number is randomly selected. The probability that it is divisible by $10$ is

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Solution

$\begin{matrix} F o r n u m b e r t o b e d i v i s i b l e b y 10 o n e p l a c e m u s t b e 0 T o t a l p o s s i b l e c o m b i n a t i o n = 6 \times 5 \times 4 \times 3 \times 2 = 30 \times 24 = 720 f a v o u r a b l e o u t c o m e = 5 \times 4 \times 3 \times 2 \times 1 = 20 \times 6 = 120 ∴ p r o b a b i l i t y = \frac{120}{720} = \frac{1}{6} \end{matrix}$

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