Answer:
Option 4 - 84
Step-by-step explanation:
Given : Permutations of the first 9 letters of the alphabet taking 6 letters at a time.
To find : The number of permutation?
Solution :
According to question we apply combination to find the number of permutations of the first 9 letters of the alphabet taking 6 letters at a time as order doesn't matter.
The combination is given by,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n=9 and r=6
[tex]^9C_6=\frac{9!}{6!(9-6)!}[/tex]
[tex]^9C_6=\frac{9\times 8\times 7\times 6!}{6!\times 3!}[/tex]
[tex]^9C_6=\frac{9\times 8\times 7}{3\times 2\times 1}[/tex]
[tex]^9C_6=3\times 4\times 7[/tex]
[tex]^9C_6=84[/tex]
Therefore, The number of permutations of the first 9 letters of the alphabet taking 6 letters at a time is 84.
So, Option 4 is correct.
