Answer:
d. 20
Step-by-step explanation:
The given question implies 5 permutation 2, i.e [tex]_{5}[/tex][tex]P_{2}[/tex].
But,
[tex]_{n}[/tex][tex]P_{r}[/tex] = [tex]\frac{n!}{(n - r)!}[/tex]
So that for [tex]_{5}[/tex][tex]P_{2}[/tex], n = 5 and r = 2.
[tex]_{5}[/tex][tex]P_{2}[/tex] = [tex]\frac{5!}{(5 - 2)!}[/tex]
= [tex]\frac{5!}{3!}[/tex]
= [tex]\frac{5*4*3*2!}{3*2!}[/tex]
Cancel out 3 and 2 with respect to the numerator and denominator.
[tex]_{5}[/tex][tex]P_{2}[/tex] = 5 * 4
= 20
Therefore,
[tex]_{5}[/tex][tex]P_{2}[/tex] = 20
So that the correct option is D.
