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  4. In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together :

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Q. In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together :

Bihar CECEBihar CECE 2003

Solution:

First we placed the 21 English books in alternate position.
So, there are 22 vacant place left.
$\therefore $ The total number of ways $={ }^{22} C_{19}$
$=\frac{22 \times 21 \times 20}{3 \times 2 \times 1}$
$=1540$