- Home
- Standard 11
- Mathematics
6.Permutation and Combination
medium
$52$ પત્તામાંથી $5$ પત્તાની પસંદગીમાં બરાબર એક જ એક્કો આવે તે કેટલા પ્રકારે બને?
A
$778320$
B
$778320$
C
$778320$
D
$778320$
Solution
In a deck of $52$ cards, there are $4$ aces. A combinations of $5$ cards have to be made in which there is exactly one ace.
Then, one ace can be selected in $^{4} C_{3}$ ways and the remaining $4$ cards can be selected out of the $48$ cards in $^{48} C_{4}$ ways.
Thus, by multiplication principle, required number of $5$ card combinations $=\,^{48} C_{4} \times \,^{4} C_{1}=\frac{48 !}{4 ! 44 !} \times \frac{4 !}{1 ! 3 !}$
$=\frac{48 \times 47 \times 46 \times 45}{4 \times 3 \times 2 \times 1} \times 4 !$
$=778320$
Standard 11
Mathematics
