Question:
In how many ways can the letters of the word COCHIN be arranged such that the two 'C's are never separated by any other letter?
In how many ways can the letters of the word COCHIN be arranged such that the two 'C's are never separated by any other letter?
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Always read the constraint carefully! The phrase "never separated" is just a clever linguistic trick to say "always together". Don't waste time calculating total permutations and subtracting like you would for a "never together" constraint problem.
Updated On: May 26, 2026
- \( 360 \)
- \( 120 \)
- \( 240 \)
- \( 720 \)
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The Correct Option is B
Solution and Explanation
Concept:
The condition that the two 'C's must "never be separated" means that they must always stay together as an unbroken sequence block. Just like the BITSAT question, we deploy the String/Bundling Method here.
Step 1: Grouping the components into a single unit.
The word is COCHIN, containing 6 total letters: C, O, C, H, I, N (where 'C' is repeated twice). Since both 'C's must be positioned together, we lock them inside a single composite structural block: \(\text{[CC]}\). Now, we count this bundle as a single item along with the remaining individual letters: \[ \text{O, H, I, N, [CC]} \] This gives us a total of 5 distinct independent items to shuffle around.
Step 2: Calculating total valid arrangements.
The number of ways to linearly arrange these 5 distinct entities is: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \text{ ways} \] Inside the block \(\text{[CC]}\), because both letters are completely identical, swapping their relative positions creates zero new visible words (\(\frac{2!}{2!} = 1\) configuration). Therefore, the total number of permutations is: \[ 120 \times 1 = 120 \text{ ways} \]
Step 1: Grouping the components into a single unit.
The word is COCHIN, containing 6 total letters: C, O, C, H, I, N (where 'C' is repeated twice). Since both 'C's must be positioned together, we lock them inside a single composite structural block: \(\text{[CC]}\). Now, we count this bundle as a single item along with the remaining individual letters: \[ \text{O, H, I, N, [CC]} \] This gives us a total of 5 distinct independent items to shuffle around.
Step 2: Calculating total valid arrangements.
The number of ways to linearly arrange these 5 distinct entities is: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \text{ ways} \] Inside the block \(\text{[CC]}\), because both letters are completely identical, swapping their relative positions creates zero new visible words (\(\frac{2!}{2!} = 1\) configuration). Therefore, the total number of permutations is: \[ 120 \times 1 = 120 \text{ ways} \]
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