The least value of natural number n satisfying Cn,5+Cn,6>Cn+1,5 is?
11
10
12
13
Calculate the value of n based on given information
The given inequality is,
Cn,5+Cn,6>Cn+1,5
⇒ C5n+C6n>C5n+1
⇒ C6n+C5n>C5n+1
⇒ C6n+1>C5n+1 …∵Crn+Cr-1n=Crn+1
⇒ n+1!6!n+1-6!>n+1!5!n+1-5! …∵Crn=n!r!n-r!
⇒ n+1!6×5!×n+1-6!>n+1!5!n+1-5×n+1-6!
⇒ 16>1n-4
⇒ n-4>6
⇒ n>6+4
⇒ n>10
Thus, the least value of n is 11.
Hence, option A is the correct option.
For what least value of n where n is the natural number: 24n is divisible by 8 .
For what least value of n where n is natural number: (5)n is divisible by 3.