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)=[tex]\frac{10!}{3!(10-3)!}[/tex]
By using combination formula: [tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]C(10,3)=\frac{10!}{3!7!}[/tex]
a.C(3,10)
We have n=3, r=10
C(3,10)=[tex]\frac{3!}{10!(3-10)!}=\frac{3!}{10!(-7)!}[/tex]
It is not possible because n factorial is the product of n natural numbers.
b.C(10,7)
[tex]C(10,7)=\frac{10!}{7!(10-7)!}=\frac{10!}{7!3!}[/tex]
Therefore, C(10,7)=C(10,3)
c.P(10,3)
[tex]P(n,r)=nP_r=\frac{n!(n-r)!}[/tex]
[tex]P(10,3)=\frac{10!}{(10-3)!}=\frac{10!}{7!}[/tex]
Therefore, C(10,3)[tex]\neq P(10,3)[/tex]
Answer:C(10,7)
