In how many ways can the letters of the word 'QUANTITATIVE' be arranged, so that all T are together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 907200
Letters that must stay together are tied into one block and the block is arranged with the other letters. Repeated letters are allowed for by dividing by the factorial of each repeat.
The letters of QUANTITATIVE (12 in all):
T three times, A twice, I twice
Q, U, N, V, E once each
The arrangement (the three T’s as one block):
Units to arrange: the TTT block + 9 other letters \(=10\)
Among them A and I repeat twice each
Arrangements \(\displaystyle =\frac{10!}{2!\times2!}=\frac{3628800}{4}=907200\)
The three T’s are alike, so the block has only one inner order and nothing more is multiplied.