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1. C(8,3)=56
2. N=6.
3. C(9,9)= 1.
1. C(8,3) =
C(8,3) =
C(8,3) = 56
2. C(n,4)=15
Substitute the values for r and C(n,r)
Simplifying, we have
Multiplication Property of Equality
Factorial definition
Since, (n-4)! divided by itself is 1, then,
Since there are four factors on the other side, factor 360 into four such that the factors are decreasing consecutive positive integers.
n(n-1)(n-2)(n-3)=(6)(5)(4)(3)
Both sides are now in consecutive order. So, N=6.
3. C(h,k) = h! / k! (h-k)!
C(9,9) = 9! / 9! (9-9)!
C(9,9) = 9! / 9! (0!)
Note: Remember that 0! = 1
C(9,9) = 9! / 9!
C(9,9) = 1