Respuesta :
Given that Mr. Jones owns 4 pairs of pants, 7 shirts, and 3 sweaters. We are asked to find the number of ways he can choose 2 pairs of pants, 3 shirts, and 1 sweater for a trip.
Explanation
The question above is a case of selection that refers to Combination. We will be using the formula below.
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Therefore, we will apply the above formula to solve the question.
[tex]^4C_2\times^7C_3\times^3C_1[/tex]This implies that there are C(4,2) = 6 ways to choose 2 pairs of pants. There are C(7,3) = 35 ways to choose 3 shirts. There are C(3,1) = 3 ways to choose a sweater. So in total, there are
[tex]\begin{gathered} =\frac{4!}{2!2!}\times\frac{7!}{3!4!}\times\frac{3!}{1!2!} \\ =6\times35\times3=630 \end{gathered}[/tex]Answer: 630 ways
