How many ways letters of word ‘CHEKOSLOVAKIA’ can be arranged so that “SL” always comes together and ‘H’ and ‘I’ at end?

Question

In how many ways the letters of the word ‘CHEKOSLOVAKIA’ can be arranged such that “SL” always comes together and ‘H’ and ‘I’ at the end places?

Answer 1

(H)CEKO(SL)OVAKA(I)
CEKO(SL)OVAKA ===> 10!/(2!*2!*2!) = 453600
(H)CEKO(SL)OVAKA(I) ===> 453600*2 = 907200.

Comments

SL comes together but their arrangement can also changed. so shouldn't it be multiply by 2 also?

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I assumed that 'SL' have to be there in the given order. So you are right if 'LS' is allowed.