How-many-password-containing-6-characters-of-the-letters-in-the-word-Move-Now-

Question Number 130685 by EDWIN88 last updated on 28/Jan/21

H o w m a n y p a s s w o r d c o n t a i n i n g

6 c h a r a c t e r s o f t h e l e t t e r s i n t h e

w o r d^{″} M o v e N o w^{″} ?

Answered by liberty last updated on 28/Jan/21

case (1) \underline{O} \underline{} \underline{} \underline{} \underset{- -}{} = 6!

case (2) \underline{O} \underline{O} \underline{} \underline{} \underline{} \underline{} = C_{4}^{5} \times \frac{6!}{2!} = 5 \times \frac{6!}{2}

totally many password is 6! + \frac{5}{2} \times 6!

= 6! (\frac{7}{2}) = 2520

Answered by JDamian last updated on 28/Jan/21

P e r m u t a t i o n s w i t h r e p e t i t i o n

\frac{7!}{2!} = \frac{7!}{2}

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