Home
Class 12
MATHS
If ^n+2C8:^(n-2)P4: 57 : 16 , find ndot...

If `^n+2C_8:^(n-2)P_4: 57 : 16 ,` find `ndot`

Text Solution

Verified by Experts

The correct Answer is:
19
We have
`.^(n+2)C_(8): .^(n-2)P_(4)=57: 16`
or `( .^(n+2)C_(8))/(.^(n-2)P_(4))=(57)/(16)`
or `((n+2)!)/(8!(n-6)!)xx((n-6)!)/((n-2)!)=(57)/(16)`
or `(n+2)(n+1)n(n-1)=(57)/(16)xx8!`
`=(19xx3)/(16)xx8xx7xx6xx5xx4xx3xx2xx1`
`implies (n-1)n(n+1)(n+2)=18xx19xx20xx21`
or n-1=18
or n=19
Promotional Banner

Similar Questions

Explore conceptually related problems

If .^(n+2)C_8:^(n-2)P_4:: 57 : 16 , find n

If the ratio .^2n C_3:^n C_3 is equal to 11:1 find ndot

If .^(2n+1)P_(n-1): .^(2n-1)P_(n)=3:5 , find n.

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If .^(n)C_(8)=.^(n)C_(6) , then find .^(n)C_(2) .

If .^(n)C_(5)=.^(n)C_(4) , then find .^(n)C_(7) .

If .^(n+1)C_n=16 , then find n.

If ""^(n)C_(8)=""^(n)C_(2) , find ""^(n)C_(2) .

If .^(n)C_(4)=.^(n)C_(2) , then find .^(n)C_(3) .

If .^(n)C_(7)=.^(n)C_(2) , then find .^(n)C_(2) .