If any four numbers are selected and they are multiplied, then probability that last digit will be 1

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14.Probability

easy

If any four numbers are selected and they are multiplied, then the probability that the last digit will be $1, 3, 5$ or $7$ is

A

$\frac{4}{{625}}$

B

$\frac{{18}}{{625}}$

C

$\frac{{16}}{{625}}$

D

None of these

Solution

(c) Total number of digits in any number at the unit place is $10$.

$\therefore $ $n(S) = 10$

To get the last digit in product is $1, 3, 5$ or $7$, it is necessary the last digit in each number must be $1, 3, 5$ or $7$.

$\therefore$ $n (A) = 4$,

$\therefore $ $P (A)$ = $\frac{4}{{10}} = \frac{2}{5}$

$\therefore$ Required probability $ = {\left( {\frac{2}{5}} \right)^4} = \frac{{16}}{{625}}$.

Standard 11

Mathematics

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