- Home
- Standard 11
- Mathematics
6.Permutation and Combination
medium
$52$ પત્તાંઓમાંથી $4$ પત્તાં કેટલા પ્રકારે પસંદ કરી શકાય ? આમાંથી કેટલા પ્રકારની પસંદગીમાં, પત્તાં સમાન રંગોવાળાં હોય ?
A
$29900$
B
$29900$
C
$29900$
D
$29900$
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 $=\,^{52} C _{4}=\frac{52 !}{4 ! 48 !}=\frac{49 \times 50 \times 51 \times 52}{2 \times 3 \times 4}$
$=270725$
$4$ red cards can be selected out of $26$ red cards in $^{26} C _{4}$ ways.
$4$ black cards can be selected out of $26$ black cards in $^{26} C _{4}$ ways.
Therefore, the required number of ways $=\,^{26} C _{4}+^{26} C _{4}$
$=2 \times \frac{26 !}{4 ! 22 !}=29900$
Standard 11
Mathematics
