The letters of the word ‘JUMBLE’ are arranged at random. Find the probability of having exactly two letters in between N and R.
Explanation:
There are 6 letters in the word JUMBLE. Apart from N and R there are 4 more letters.
Arranging J, E and two letters between them. Let us first choose which two letters will be between J and E This can be done in 4C2 = 6 ways. These two letters can be arranged in 2! = 2 ways. J and E can also be arranged in 2! = 2 ways. ⇒ Total ways of arranging J, E and two letters in between them = 6 × 2 × 2 = 24 ways. Let us call this arrangement X.
Now we have to arrange X and two remaining letters. This can be done in 3! = 6 ways.
⇒ Total ways of arranging the letters of the word JUMBLE such that there are exactly two letters in between J and E = 24 × 6 = 144
Total ways of arranging the letters of the word JUMBLE = 6! = 720
∴ Required probability = 144/720 = 1/5
Hence, option (a).
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