How many permutations can be formed with the letters of the word `PARTICLE` so that T and I always remain together
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1
Total number of words that can be formed from the letters PARTICLE so that T an I remain together
= 6! x 2
= 6! x 2
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Solution :-
The given word is PARTICLE
Total number of letters in the word PARTICLE = 8
We always have to put T and I together. So, T and I will be considered as 1 letter. T and I can be arranged together and I and T can also be arranged together. T and I and I and T can be arranged in 2 different ways.
Therefore, remaining letters = 8 - 1 = 7
7 letters can be arranged in 7 different ways
So, total number of permutations = 7! × 2!
⇒ (7*6*5*4*3*2*1)*(2*1)
⇒ 5040*2
⇒ 10080 permutations can be formed with the word PARTICLE so that T and I always remain together.
Answer.
The given word is PARTICLE
Total number of letters in the word PARTICLE = 8
We always have to put T and I together. So, T and I will be considered as 1 letter. T and I can be arranged together and I and T can also be arranged together. T and I and I and T can be arranged in 2 different ways.
Therefore, remaining letters = 8 - 1 = 7
7 letters can be arranged in 7 different ways
So, total number of permutations = 7! × 2!
⇒ (7*6*5*4*3*2*1)*(2*1)
⇒ 5040*2
⇒ 10080 permutations can be formed with the word PARTICLE so that T and I always remain together.
Answer.
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