Which is an incorrect way of writing 10C3 ?

Question

Which is an incorrect way of writing ₁₀C₃? Please explain why for each thank you.

A. ₁₀P₃ / 3!

B. ₁₀P₃ / 7!

C. 10! / 3!7!

Answer 1

10C3 = 10*9*8/(1*2*3)= 120

Now check option C

10!/( 3! *7!)

= 10*9*8*7*6*5*4*3*2*1/ ( 3*2*1) (7*6*5*4*3*2*1)

= 10*9*8 /(3*2*1)= 10*3*4 = 120