Question

MAT / mat 521 Homework 1: Problem 6 2 points) A boy has 2 red, 4 yellow and 5 green marbles. In how

Answer 1

Solution:

A boy has 2 red, 4 yellow and 5 green marbles. In how many ways can the boy arrange the marbles in a line if:

a) Marbles of the same color are indistinguishable?

Answer: $\dpi{100} \large \boldsymbol{6930 }$

Explanation:

Number of red marbles = 2

Number of yellow marbles = 4

Number of green marbles = 5

Therefore, the total number of marbles is = 2+4+5 =11

Since the marbles of the same color are indistinguishable, hence the number of possible arrangements is:

$\dpi{100} \large \frac{11!}{2! \times 4! \times 5!}=\frac{39916800}{2 \times 24 \times 120}=6930$

b) All marbles have different sizes.

Answer: $\dpi{100} \large \boldsymbol{39916800}$

Explanation:

Since all the marbles have different size, therefore, the number of possible arrangements is:

$\dpi{100} \large 11!=39916800$