In a shelf there are $10$ English and $8$ Telugu books. The number of ways in which $6$ books can be chosen if a particular English book is excluded and a particular Telugu book is excluded is:

^{9} C_{3} .^{7} C_{3}

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^{16} C_{6}

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^{9} C_{3} .^{8} C_{3}

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^{18} C_{8}

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Solution

The correct option is A $^{16} C_{6}$
Total number of books in the shelf is $18$ , but we have to select $6$ books only which can be selected in $^{18} C_{6}$ ways, but this is not the correct answer.
As it is also mentioned that you have to exclude two particular books one of Telugu and one of English, so your sample space get reduced by two.
$∴$ Required number of ways $=^{18 - 2} C_{6} =^{16} C_{6}$

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