Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word FLOWERS.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 FLOWERS.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
Sure, I can help with that.
a. The number of ways you can arrange all of the letters in the word FLOWERS is calculated by finding the factorial of the number of letters. The word FLOWERS has 7 letters, so the number of arrangements is 7! (7 factorial), which is 7654321 = 5040.
b. The number of ways you can arrange two of the letters in the word FLOWERS is calculated by using the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!. Here, n is the total number of letters (7) and r is the number of letters we are choosing (2). So, the number of arrangements is 7P2 = 7! / (7-2)! = 7*6 = 42.
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