What is the number of arrangements that can be made with the letters of the word CAREFUL so that the vowels occupy even places?Question 2Answera.144b.120c.720d.36

To find the number of arrangements where the vowels (A, E, U) occupy even places in the word CAREFUL, we need to consider the positions of the vowels and the consonants separately.

Step 1: Count the number of vowels in the word CAREFUL. We have three vowels: A, E, and U.

Step 2: Determine the number of even positions in the word CAREFUL. The word has six letters, so there are three even positions: 2nd, 4th, and 6th.

Step 3: Calculate the number of arrangements for the vowels in the even positions. Since we have three vowels, we can arrange them in 3! (3 factorial) ways.

Step 4: Calculate the number of arrangements for the consonants in the remaining positions. The word CAREFUL has four consonants: C, R, F, and L. We can arrange them in 4! (4 factorial) ways.

Step 5: Multiply the number of arrangements for the vowels and the consonants together to get the total number of arrangements. So, the total number of arrangements is 3! * 4! = 6 * 24 = 144.

Therefore, the number of arrangements that can be made with the letters of the word CAREFUL, where the vowels occupy even places, is 144.

Hence, the correct answer is option a. 144.