The Solution:
Given:
7 students from the Junior class.
6 students from the Senior class.
4 new members are to be chosen.
Required:
Find the number of ways 4 new members can be chosen if 2 or fewer must be from the senior class.
So, the possibilities are:
[tex]\begin{gathered} (^6C_0\cdot^7C_4)\text{ or }(^6C_1\cdot^7C_3)\text{ or }(^6C_2\cdot^7C_2) \\ \\ (^6C_0\cdot^7C_4)+(^6C_1\cdot^7C_3)+(^6C_2\cdot^7C_2) \end{gathered}[/tex]By formula, Combination is
So,
[tex]\lbrack\frac{6!}{(6-0)!0!}\times\frac{7!}{(7-4)!4!}\rbrack+\lbrack\frac{6!}{(6-1)!1!}\times\frac{7!}{(7-3)!3!}\rbrack+\lbrack\frac{6!}{(6-2)!2!}\times\frac{7!}{(7-2)!2!}\rbrack[/tex][tex]=(1\times35)+(6\times35)+(15\times21)=35+210+315=560\text{ ways}[/tex]Therefore, the correct answer is 560 ways.
