Given as
The word ‘PARALLEL’
Here's are 8 letters in the word ‘PARALLEL’ out of which 2 are A’s, 3 are L’s and the rest all are distinct.
Therefore by using the formula,
n!/ (p! × q! × r!)
The total number of arrangements = 8! / (2! 3!)
= [8 × 7 × 6 × 5 × 4 × 3 × 2 × 1] / (2 × 1 × 3 × 2 ×1)
= 8 × 7 × 5 × 4 × 3 × 1
= 3360
Then, let us consider all L’s together as one letter, therefore we have 6 letters out of which A repeats 2 times and others are distinct.
These 6 letters can be arranged in 6! / 2! Ways.
Number of words in which all L’s come together = 6! / 2!
= [6 × 5 × 4 × 3 × 2 × 1] / (2 × 1)
= 6 × 5 × 4 × 3
= 360
Therefore, now the number of words in which all L’s do not come together = total number of arrangements – The number of words in which all L’s come together
= 3360 – 360 = 3000
