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Question

The number of ways in which any four letters can be selected from the word 'CORGOO' is :


A
15
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B
11
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C
7
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D
None of these
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Solution

The correct option is C $$7$$
Since there are three $$O$$'s. Atleast one '$$O$$' shoilf be there in the selected four letters.
Hence there are three cases:
$$Case 1:$$  Only one $$O$$ is present
Number of Selections = 1 (Since we have to select all three remaning letters)
$$ Case 2:$$ Two $$O$$'s 
Number of Selections = 3 (two of the remaining 3 letters have to be selected)
$$ Case 3:$$ Three $$O$$'s 
Number of Selections = 3 (one of the remaining 3 letters have to be selected)

Therefore total number of selections is $$1+3+3=7$$ 

Maths

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