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