To solve this problem, we first consider the word 'CORPORATION' as 'CRPRTN (OAOIO)'. Here, we are treating the vowels OAOIO as a single letter.

Step 1: Count the number of letters in the modified word 'CRPRTN (OAOIO)'. There are 7 letters, but we have 2 Rs and 3 Os. So, the number of ways to arrange these letters is 7!/(2!*3!) = 2520 ways.

Step 2: Now, consider the vowels OAOIO. There are 5 vowels, but we have 3 Os and 2 Os. So, the number of ways to arrange these vowels is 5!/(3!*2!) = 10 ways.

Step 3: Since the vowels and the rest of the letters can be arranged independently, we multiply the number of arrangements from step 1 and step 2. So, the total number of ways to arrange the letters in the word 'CORPORATION' such that the vowels always come together is 2520 * 10 = 25200 ways.

So, the correct answer is not in the given choices.

Question

To solve this problem, we first consider the word 'CORPORATION' as 'CRPRTN (OAOIO)'. Here, we are treating the vowels OAOIO as a single letter.

Step 1: Count the number of letters in the modified word 'CRPRTN (OAOIO)'. There are 7 letters, but we have 2 Rs and 3 Os. So, the number of ways to arrange these letters is 7!/(2!*3!) = 2520 ways.

Step 2: Now, consider the vowels OAOIO. There are 5 vowels, but we have 3 Os and 2 Os. So, the number of ways to arrange these vowels is 5!/(3!*2!) = 10 ways.

Step 3: Since the vowels and the rest of the letters can be arranged independently, we multiply the number of arrangements from step 1 and step 2. So, the total number of ways to arrange the letters in the word 'CORPORATION' such that the vowels always come together is 2520 * 10 = 25200 ways.

So, the correct answer is not in the given choices.

Knowee AI · Accepted Answer

To solve this problem, we first consider the word 'CORPORATION' as 'CRPRTN (OAOIO)'. Here, we are treating the vowels OAOIO as a single letter.

Step 1: Count the number of letters in the modified word 'CRPRTN (OAOIO)'. There are 7 letters, but we have 2 Rs and 3 Os. So, the number of ways to arrange these letters is 7!/(2!*3!) = 2520 ways.

Step 2: Now, consider the vowels OAOIO. There are 5 vowels, but we have 3 Os and 2 Os. So, the number of ways to arrange these vowels is 5!/(3!*2!) = 10 ways.

Step 3: Since the vowels and the rest of the letters can be arranged independently, we multiply the number of arrangements from step 1 and step 2. So, the total number of ways to arrange the letters in the word 'CORPORATION' such that the vowels always come together is 2520 * 10 = 25200 ways.

So, the correct answer is not in the given choices.

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?Choices:- 1440 50400 2070 2880

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