Question

select the correct answer from each drop - down menu. a high school auditorium seats 110 people. the school play has 106 people in attendance leaving 4 seats empty. the order in which the seats are chosen is not important, so this is drop - down menu with options combination, permutation. there are drop - down menu ways that 4 seats can be left empty in the auditorium.

Explanation:

Step1: Identify selection type

Since order does not matter, this is a combination problem. The formula for combinations is:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=110$ (total seats), $k=4$ (empty seats).

Step2: Substitute values into formula

$$C(110,4)=\frac{110!}{4!(110-4)!}=\frac{110\times109\times108\times107}{4\times3\times2\times1}$$

Step3: Calculate the result

First compute numerator: $110\times109=11990$, $108\times107=11556$, $11990\times11556=138556440$
Denominator: $4\times3\times2\times1=24$
$$\frac{138556440}{24}=5773185$$

Answer:

First dropdown: combination
Second blank: 5773185