twelve education students, in groups of four, are taking part in a student - teacher program. mark cannot be…

twelve education students, in groups of four, are taking part in a student - teacher program. mark cannot be in the first group because he will be arriving late. how many ways can the instructor choose the first group of four education students?\n220\n330\n1,980\n7,920

twelve education students, in groups of four, are taking part in a student - teacher program. mark cannot be in the first group because he will be arriving late. how many ways can the instructor choose the first group of four education students?\n220\n330\n1,980\n7,920

Answer

Explanation:

Step1: Determine available students

Since Mark cannot be in the first - group, there are 11 available students for the first group of 4.

Step2: Use combination formula

The number of combinations of (n) items taken (r) at a time is (C(n,r)=\frac{n!}{r!(n - r)!}). Here (n = 11) and (r=4). [C(11,4)=\frac{11!}{4!(11 - 4)!}=\frac{11!}{4!7!}] [=\frac{11\times10\times9\times8\times7!}{4\times3\times2\times1\times7!}] [=\frac{11\times10\times9\times8}{4\times3\times2\times1}] [ = 330]

Answer:

330