Respuesta :
There are 120 combinations.
There are 4 ways she can choose the math class; 2 ways to choose the science class; 3 ways to choose the language class; and 5 ways to choose the art class:
4(2)(3)(5) = 120
There are 4 ways she can choose the math class; 2 ways to choose the science class; 3 ways to choose the language class; and 5 ways to choose the art class:
4(2)(3)(5) = 120
Answer: The total number of different combinations of classes is 120.
Step-by-step explanation: Given that Brunette College offers 4 math classes, 2 science classes, 3 language classes and 5 art classes. Sylvia needs to sign up for exactly one class in each subject.
We are to find the number of different combinations of classes does Sylvia have to choose from.
We will be using the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]
Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be
[tex]^4C_1\times ^2C_1\times ^3C_1\times ^5C_1\\\\=\dfrac{4!}{1!(4-1)!}\times \dfrac{2!}{1!(2-1)!}\times \dfrac{3!}{1!(3-1)!}\times \dfrac{5!}{1!(5-1)!}\times\\\\\\=\dfrac{4\times 3!}{1\times 3!}\times \dfrac{2\times 1!}{1\times 1!}\times \dfrac{3\times 2!}{1\times 2!}\times \dfrac{5\times 4!}{1\times 4!}\\\\=4\times 2\times 3\times 5\\\\=120.[/tex]
Thus, the total number of different combinations is 120.
