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PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS AND COMBINATIONS4 Marks
Question
What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these four cards belong to four different suits.
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Answer

There are 13 cards in each suit. Thus, there are ${ }^{13} \mathrm{C}_1$ ways of choosing 1 card from 13 cards of diamond, ${ }^{13} \mathrm{C}_1$ ways of choosing 1 card from 13 cards of hearts, ${ }^{13} \mathrm{C}_1$ ways of choosing 1 card from 13 cards of clubs, ${ }^{13} \mathrm{C}_1$ ways of choosing 1 card from 13 cards of spades. Thus, by multiplication principle, therefore the required number of ways
$ = ^{13} C_{1} \times^{13} C_{1} \times^{13} C_{1} \times^{13} C_{1} $
$ =13 \times 13 \times 13 \times 13 $
$= 13^4$

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