## Quant Question Of The Day : 9

[latexpage]

# Counting

In how many ways we can select 6 letters out of the eight letters of the word ‘TATHAGAT’?

1. 12

2. 16

3. 8

4. None of these

Categories:
Quant question of the day, Question of the day

[latexpage]

In how many ways we can select 6 letters out of the eight letters of the word ‘TATHAGAT’?

1. 12

2. 16

3. 8

4. None of these

In TATHAGAT, we have 3 T’s, 3 A’s, 1 H and 1 G.

Now to select 6 letters out of 8 is same as to deselect remaining 2. So we just need to calculate the number of ways to select 2 letters out of the letters of the word TATHAGAT.

Case-I: Both the 2 letters are distinct – out of 4 distinct letters, we can select 2 distinct in ^{4}C_{2} = 6 ways.

Case-II: Both the 2 letters are same – the same 2 letters can be 2 T’s or 2 A’s only i.e. 2 ways.

So total required number of ways are = 6 + 2 = 8.

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