Video Transcript
Which of the following is equal to
41 𝐶 five? Is it (A) 41 𝑃 five divided by five
factorial, (B) 41 𝑃 five divided by five, (C) 41 𝑃 five multiplied by five
factorial, or (D) 41 𝑃 five multiplied by five?
We begin by recalling our formulae
for permutation and combination. The permutation 𝑛𝑃𝑘 is equal to
𝑛 factorial divided by 𝑛 minus 𝑘 factorial. And the combination 𝑛𝐶𝑘 is equal
to 𝑛 factorial divided by 𝑛 minus 𝑘 factorial multiplied by 𝑘 factorial. Combining these two formulae, we
see that 𝑛𝐶𝑘 is equal to 𝑛𝑃𝑘 divided by 𝑘 factorial. In this question, 𝑛 is equal to 41
and 𝑘 is equal to five. This means that 41 𝐶 five is equal
to 41 𝑃 five divided by five factorial. The correct answer is therefore
option (A).
