Question

enter the correct answer in the box.
an algebra class has 21 students who all participate in a welcome activity introducing themselves to each other in pairs. one student wants to know how many introductions were made.
fill in the values of n and r to complete the formula for finding the number of combinations of introductions.
\\(\frac{n!}{r!(n - r)!}\\)

Explanation:

Step1: Identify total students ($n$)

$n=21$

Step2: Identify pair size ($r$)

$r=2$

Step3: Verify combination formula fit

The formula $\frac{n!}{r!(n-r)!}$ counts unordered pairs, which matches the introduction scenario where a pair (A,B) is the same as (B,A).

Answer:

$n=21$, $r=2$