Consider the word "GOOGLE". Among all the 6 letter word that are formed using all the letter of word "GOOGLE", a word is randomly selected. The probability that O's remain between G's in the randomly selected word, is

Question

Consider the word "GOOGLE". Among all the 6 letter word that are formed using all the letter of word "GOOGLE", a word is randomly selected. The probability that O's remain between G's in the randomly selected word, is (A)  (1/6) (B) (1/3) (C) (1/9) (D) (1/18)

Tardigrade Admin · Accepted Answer

GOOGLE n ( S )=(6 !/2 ! ⋅ 2 !)=180 - G - O - O - G - n ( A )= 5 C 1 × 2 !+ 5 C 2 × 2 !=30 ∴ P ( E )=(30/180)=(1/6)

Q. Consider the word "GOOGLE". Among all the 6 letter word that are formed using all the letter of word "GOOGLE", a word is randomly selected. The probability that O's remain between G's in the randomly selected word, is

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{1}{18}$

GOOGLE
$n (S) = \frac{6 !}{2 ! \cdot 2 !} = 180$
$- G - O - O - G -$
$n (A) =^{5} C_{1} \times 2! +^{5} C_{2} \times 2! = 30$
$∴ P (E) = \frac{30}{180} = \frac{1}{6}$