From a set of 6 math, 8 science, 4 lit books, how many ways can a student select 2 from each?

Question

It's a math question can anyone tell me the correct answer. It's mostly Finite Math.

Answer 1

Each time the student will pick 6 books, 2 of each type. I'll write out all possible selections for the "lit" books (4 to choose from):

1,2
1,3
1,4
2,3
2,4
3,4

Total of 6 possible combinations.
The formula for figuring out the number of possible combinations is:
x * (x-1) / 2
4 * (4-1) / 2 = 6

For the other types of books, the formula works out like this:
math = 6 books = 15 combinations
science = 8 books = 28 combinations

Now it's simple to calculate the rest since we're grabbing the books from different categories, we just multiply the number of combinations to get the total number of possibilities.

Total = 6 * 15 * 28 = 2520

Answer 2

for the math books, you calculate how many combinations there are of 2 books taken from a group of 6. The answer is 15. To calculate that, it's 6!/2!(6-2)! = 6!/(2!x4!) = 6x5x4x3x2x1/2x1x4x3x2x1 = 30/2 = 15.

Use the same formula for the 8 science books 8!/2!(6!) = 56/2 - 28

For the lit books, is 4!/(2!x 2!) = 6

So if there are 15 possible combinations of math books, 28 combinations of science books, and 6 combinations of lit books, there are 15 x 28 x 6 ways to select two of each book, or 2520 ways to select two of each.

Answer 3

6*2=12
8*2=16
4*2=8

16*12*8=1536

1536 ways to choose those books.

Answer 4

6choose2 * 8choose2 * 4choose2

=[(6!) / (4!*2!) ] * [(8!) / (6!*2!)] * [(4!) / (2!*2!)]

=[(6*5*4*3*2*1)/(4*3*2*1 * 2*1)] *
[(8*7*6*5*4*3*2*1)/(6*5*4*3*2*1 * 2*1)] *
[(4*3*2*1) / (2*1 * 2*1)]

=[(6*5)/(2*1)] * [(8*7)/(2*1)] * [(4*3)/(2*1)]
=15 * 28 * 6 = 2520

Answer 5

i think you multiply all of the numbers, i'm pretty sure you do it that way