A five digit number is formed by writing digits 1, 2, 3, 4, 5 in a random order without repetitions.

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14.Probability

medium

A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is

$\frac{3}{5}$

$\frac{{18}}{5}$

$\frac{1}{5}$

$\frac{6}{5}$

Solution

(c) The number is divisible by $4$ if last two digits are $12, 24, 32$ and $52$. Remaining three places can be filled by $3!$ ways.
$\therefore $ Favouable cases = $3\,!\,\, \times \,\,4$
Required probability = $\frac{{3\,!\,\, \times 4}}{{5!}} = \frac{1}{5}$.

Standard 11

Mathematics

Three cards are drawn at random from a pack of $52$ cards. What is the chance of drawing three aces

easy

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easy

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $\mathrm{A}\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is

hard

(IIT-2010)

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medium

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