Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word FAMILY.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 FAMILY.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 FAMILY has 6 letters in total, with no repetitions. The number of ways to arrange all the letters is given by the factorial of the total number of letters, which is 6!. So, the number of ways to arrange all the letters in the word FAMILY is 65432*1 = 720 ways.
b. If we are only arranging two letters from the word FAMILY, we have 6 options for the first letter and 5 options for the second letter (since we can't repeat a letter). So, the number of ways to arrange two of the letters in the word FAMILY is 6*5 = 30 ways.
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