Question

A student planning her curriculum for the upcoming year must select one of four business courses, one of five mathematics courses, two of six elective courses, and either one of four history courses or one of three social science courses. How many different curricula are available for her consideration?

Answer 1

Answer: 525

Step-by-step explanation:

Given : A student planning her curriculum for the upcoming year must select one of four business courses :

One of five mathematics courses, two of six elective courses, and either one of four history courses or one of three social science courses.

Then , the number of  different curricula are available for her consideration will be :

$^5C_1\times ^6C_2\times(^4C_1+^3C_1)\\\\=5\times\dfrac{6!}{2!(6-2)!}\times(4+3)\\\\=5\times\dfrac{6\times5\times4!}{2\times4!}\times7\ \ [\because ^nC_1=n]\\\\=5\times3\times5\times7=525$

Hence, there are 525 different curricula are available for her consideration .