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  4. The number of permutations of the alphabets of the word “GOOGLE” in which O’s are together but G’s are separated, is

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Q. The number of permutations of the alphabets of the word $“GOOGLE”$ in which $O’s$ are together but $G’s$ are separated, is

NTA AbhyasNTA Abhyas 2020Permutations and Combinations

Solution:

$O’s$ together, then apart from $G’s$ other alphabets can be arranged in $3!=6$ ways. In the gaps, two $G’s$ can be placed in $\_{}^{4}C_{2}$ ways.
$\left|\boxed{OO}\right|L\left|E\right|$
Hence, the total number of ways $=3!\cdot ^{4}C_{2}=36$