Question

A classic counting problem is to determine the number of different ways that the letters of millennium can be arranged. Find that number. The number of different ways that the letters of millennium can be arranged is

Answer 1

Answer:

The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of letters of the word "millennium" = 10

Letters repeated:

m = 2 times

i = 2 times

l = 2 times

n = 2 times

2. The number of different ways that the letters of millennium can be arranged is:

We will use the n! or factorial formula, this way:

10!/2! * 2! * 2! * 2!

(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) * (2 * 1) * (2 * 1) * (2 *1)

3'628,800/2*2*2*2 = 3'628,800/16 = 226,800

The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800

Answer 2

The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800

Calculation of the number of ways:

1.

Number of letters of the word "millennium" = 10

Here

Letters repeated:

m = 2 times

i = 2 times

l = 2 times

n = 2 times

2. The number of different ways should be

$= 10!\div 2! \times 2! \times 2! \times 2!\\\\= (10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)\div (2 \times 1) \times (2 \times 1) \times (2 \times 1) \times (2 \times 1)\\\\= 3'628,800\div 2 \times2 \times2 \times2\\\\ = 3'628,800\div 16$

= 226,800

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