Permeable Nation..!!!

Probability Level 4

The number of permutations of the letters of the word HINDUSTAN such that neither the pattern HIN nor DUS nor TAN appears, are

169194 166680 181434 166674

1 solution

Harshvardhan Mehta
Feb 25, 2015

Total number of permutations = $\frac{9!}{2!}$

Number of those containing ‘HIN’ = 7!

Number of those containing ‘DUS’ = $\frac{7!}{2!}$

Number of those containing ‘TAN’ = 7!

Number of those containing ‘HIN’ and ‘DUS’ = 5!

Number of those containing ‘HIN’ and ‘TAN’ = 5!

Number of those containing ‘TAN’ and ‘DUS’ = 5!

Number of those containing ‘HIN’, ‘DUS’ and ‘TAN’ = 3!

Required number = $\frac{9!}{2!}-\left(7!+7!+\frac{7!}{2!}\right) + 3 \times 5!-3! =\quad \boxed{169194}$

Perfectly done!

Upvoted!

Sravanth C. - 6 years, 3 months ago

thanks.. $\ddot\smile$

Harshvardhan Mehta - 6 years, 3 months ago

Total Number of permutations 2!/9!?

Please review

Mehul Arora - 6 years, 3 months ago

ohhh yeah some typing error.. thanks for pointing it out... $\ddot\smile$

Harshvardhan Mehta - 6 years, 3 months ago

@Harshvardhan Mehta – My Pleasure! BTW Perfectly Done!

Mehul Arora - 6 years, 3 months ago

oh! I didn't notice that, as it was similar to my work out, I just upvoted it...

Thanks for mentioning.

Sravanth C. - 6 years, 3 months ago

I didn't get why you added 3x5! Can you please explain?

Vismay Chandra - 6 years, 2 months ago

I useed 3x5! instead of adding 5! 3 times. as you can see it is occurring 3 times.

Harshvardhan Mehta - 6 years, 1 month ago

How is 'DUS'=7!/2!?

Sahil Silare - 3 years, 2 months ago