Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word WATER.a. The number of ways you can arrange all of the letters in the word is .b. The number of ways you can arrange two of the letters in the word is .
Question
Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word WATER.a. The number of ways you can arrange all of the letters in the word is .b. The number of ways you can arrange two of the letters in the word is .
Solution
a. The word WATER has 5 letters, all of which are distinct. The number of ways to arrange n distinct items is given by n factorial (n!). So, the number of ways to arrange all the letters in WATER is 5! = 54321 = 120.
b. The number of ways to arrange 2 letters out of 5 is given by the combination formula nCr = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose. Here, n=5 and r=2. So, the number of ways to arrange two of the letters in WATER is 5C2 = 5! / [(5-2)! * 2!] = 10.
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