Question Type 5: Applying formula multiple times for different groups of selection Exercises

From a shelf of 6 red books, 5 green books and 4 blue books, find the number of ways to select 2 red, 1 green and 2 blue books.

In how many ways can a committee be formed by choosing 3 men and 2 women from a group of 10 men and 8 women?

A fruit basket has 7 apples, 5 oranges and 8 bananas. How many ways can you select 2 apples, 1 orange and 2 bananas?

In a standard deck, there are 13 hearts and 13 spades. How many ways are there to choose 2 hearts and 3 spades?

A bag contains 8 red, 5 blue, and 7 green marbles. How many ways can you select 4 marbles such that exactly two are of one color and one each of the other two colors?

A school needs to choose a team of 4 students: 2 from 12 seniors and 2 from 15 juniors. How many selections are possible?

Find the number of ways to select 3 science books, 2 art books, and 1 history book.

From a pool of 15 full-time and 10 part-time employees, in how many ways can a project team of 3 full-time and 2 part-time employees be chosen?

A committee of 5 must include exactly 2 computer scientists, 1 physicist and 2 mathematicians from 6 CS, 4 physics and 5 math faculty. How many ways can this committee be formed?

Calculate the number of ways to select 2 red balls and 3 green balls from a bag containing 5 red and 6 green balls.

A box contains 4 red balls and 7 blue balls. How many ways can you select 3 red balls and 2 blue balls?

A panel is formed by selecting 1 chair from 5 professors and 3 members from 12 lecturers. How many ways can this panel be chosen?