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

Question

The number of permutations of the alphabets of the word “GOOGLE” in which O’s are together but G’s are separated, is (A) 24 (B) 48 (C) 72 (D) 36

Tardigrade Admin · Accepted Answer

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 4C2 ways. | boxedOO|L|E| Hence, the total number of ways =3!⋅ 4C2=36

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

$24$

$48$

$72$

$36$

$O ’ s$ 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.
$∣ ∣ OO ∣ ∣ L ∣ E ∣$
Hence, the total number of ways $= 3! \cdot^{4} C_{2} = 36$

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

24

48

72

36