Question

If rcr-1= 56, ncr = 28 and ncr+1 = 8, then r is equal to
8
6
5​

Answer 1

Answer:

From the given information,

n

C

r

n

C

r−1

=2

⇒

(r−1)!(n−(r−1))!.n!

n!r!(n−r)!

=2

⇒

n+1−r

r

=2

⇒r=2n+2−2r

⇒3r=2n+2...(i)

Also,

n

C

r+1

n

C

r

=

2

7

⇒

n!.r!.(n−r)!

n!(n−(r+1))!.(r+1)!

=

2

7

⇒

n−r

r+1

=

2

7

⇒2r+2=7n−7r

⇒9r=7n−2 ...(ii)

⇒n=8

Hence,

⇒9r=56−2

⇒9r=54

⇒r=6