6.Permutation and Combination
medium

$52$ પત્તાંઓમાંથી $4$ પત્તાં કેટલા પ્રકારે પસંદ કરી શકાય ? આમાંથી કેટલા પ્રકારની પસંદગીમાં, ચિત્રવાળાં પત્તાં હોય ? 

A

$495$

B

$495$

C

$495$

D

$495$

Solution

There will be as many ways of choosing $4$ cards from $52$ cards as there are combinations of $52$ different things, taken $4$ at a time. Therefore

The required number of ways $=\,\,^{52} C _{4}=\frac{52 !}{4 ! 48 !}=\frac{49 \times 50 \times 51 \times 52}{2 \times 3 \times 4}$

$=270725$

There are $12$ face cards and $4$ are to be selected out of these $12$ cards. This can be done in $^{12} C _{4}$ ways.

Therefore, the required number of ways $=\frac{12 !}{4 ! 8 !}=495$

Standard 11
Mathematics

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