If all the words that can be formed from the letters of the word GARNE are taken and arranged in alphabetical order, then the rank of the word RANGE is?

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101

100

102

Correct

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Explanation

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Official Explanation

Official

Given word: GARNE. Alphabetical order of letters: A, E, G, N, R.

Step 1: Words starting with A.

Fix A as the first letter. The remaining letters E, G, N, R can be arranged in

4! = 4 \times 3 \times 2 \times 1 = 24

ways.

Step 2: Words starting with E, G, or N.

Similarly, each of E, G, N as the first letter gives

4! = 24

words.

Total words with first letter A, E, G, or N:

24 + 24 + 24 + 24 = 96

words.

Step 3: Words starting with R.

Now consider words starting with R, in alphabetical order.…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.