To solve this problem, we need to consider the word "PUZZLE" and its vowels and consonants. The word "PUZZLE" has 6 letters, with 2 vowels (U, E) and 4 consonants (P, Z, Z, L).

Step 1: Since the vowels need to always come together, we can consider the group of vowels (UE) as a single letter. So, we have 5 "letters" to arrange: P, Z, Z, L, and UE.

Step 2: We arrange these 5 "letters" in different ways. The formula for arranging n items (with repetition) is n!. However, since the letter Z is repeated, we divide by 2! to correct for over-counting. So, the number of arrangements is 5! / 2! = 60.

Step 3: However, within the "letter" UE, the U and E can be arranged in 2! = 2 ways.

Step 4: Therefore, the total number of ways the letters of the word "PUZZLE" can be arranged such that the vowels always come together is 60 * 2 = 120.

Question

To solve this problem, we need to consider the word "PUZZLE" and its vowels and consonants. The word "PUZZLE" has 6 letters, with 2 vowels (U, E) and 4 consonants (P, Z, Z, L).

Step 1: Since the vowels need to always come together, we can consider the group of vowels (UE) as a single letter. So, we have 5 "letters" to arrange: P, Z, Z, L, and UE.

Step 2: We arrange these 5 "letters" in different ways. The formula for arranging n items (with repetition) is n!. However, since the letter Z is repeated, we divide by 2! to correct for over-counting. So, the number of arrangements is 5! / 2! = 60.

Step 3: However, within the "letter" UE, the U and E can be arranged in 2! = 2 ways.

Step 4: Therefore, the total number of ways the letters of the word "PUZZLE" can be arranged such that the vowels always come together is 60 * 2 = 120.

Knowee AI · Accepted Answer

To solve this problem, we need to consider the word "PUZZLE" and its vowels and consonants. The word "PUZZLE" has 6 letters, with 2 vowels (U, E) and 4 consonants (P, Z, Z, L).

Step 1: Since the vowels need to always come together, we can consider the group of vowels (UE) as a single letter. So, we have 5 "letters" to arrange: P, Z, Z, L, and UE.

Step 2: We arrange these 5 "letters" in different ways. The formula for arranging n items (with repetition) is n!. However, since the letter Z is repeated, we divide by 2! to correct for over-counting. So, the number of arrangements is 5! / 2! = 60.

Step 3: However, within the "letter" UE, the U and E can be arranged in 2! = 2 ways.

Step 4: Therefore, the total number of ways the letters of the word "PUZZLE" can be arranged such that the vowels always come together is 60 * 2 = 120.

In what ways the letters of the word "PUZZLE" can be arranged to form the different new words so that the vowels always come together?

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