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  • If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?

If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?

Answers (1)

ALGORITHM... (given word)

Total number of letters: 9

Thus, total number of words = 9!

Thus, n(s) = 9!

Considering ‘GOR’ as one group

A     L    GOR    I    T    H    M

↓      ↓       ↓       ↓    ↓    ↓    ↓

1      2      3       4    5   6     7

Thus, no. of letters = 7

Now, if the GOR group remains together, then the order = 7!

Thus, n (E) = 7!

Now, 

required probability = number of favourable outcomes / total number of outcomes

                                    = n (E) / n(S)    …..[Since n! = n x (n – 1) x (n – 2)…1]

                                    = 7! / 9!

                                    = 7! / 9 x 8 x 7!

                                    = 1 / 72

Posted by

infoexpert22

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