The number of numbers that can be formed with the help of the dig… - Vidyadip

MCQ

The number of numbers that can be formed with the help of the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy odd places, is

A
$24$
✓
$18$
C
$12$
D
$30$

✓

Answer

Correct option: B.

$18$

b
(b) The $4$ odd digits $1, 3, 3, 1$ can be arranged in the $4$ odd places in $\frac{{4\;!}}{{2\;!\;2\;!}} = 6$ ways and $3 $ even digits $2, 4, 2$ can be arranged in the three even places in $\frac{{3\;!}}{{2\;!}} = 3$ ways. Hence the required number of ways $ = 6 \times 3 = 18$.

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