Answer:
C(10,7)
Step-by-step explanation:
We are given that C(10, 3)
We have to find the which is equal to C(10,3) in given options.
C(10,3)=\(\frac{10!}{3!(10-3)!}\)
By using combination formula: \(nC_r=\frac{n!}{r!(n-r)!}\)
\(C(10,3)=\frac{10!}{3!7!}\)
a.C(3,10)
We have n=3, r=10
C(3,10)=\(\frac{3!}{10!(3-10)!}=\frac{3!}{10!(-7)!}\)
It is not possible because n factorial is the product of n natural numbers.
b.C(10,7)
\(C(10,7)=\frac{10!}{7!(10-7)!}=\frac{10!}{7!3!}\)
Therefore, C(10,7)=C(10,3)
c.P(10,3)
\(P(n,r)=nP_r=\frac{n!(n-r)!}\)
\(P(10,3)=\frac{10!}{(10-3)!}=\frac{10!}{7!}\)
Therefore, C(10,3)\(eq P(10,3)\)
Answer:C(10,7)
