# arrangement of word SUCCESS

#### jacks

##### Well-known member
how many number of words are formed from word $\bf{SUCCESS}$ such that no two $\bf{C}$ and no two $\bf{S}$ are together

My Trial:: First we will count Total no. of arrangement of words without restriction.

which is $\displaystyle = \frac{7!}{3!\times 2!} = 420$

Now Total no. of arrangement in which two $\bf{C}$ are together

which is $\displaystyle = \frac{6!}{3!} = 120$

Now Total no. of words in which no two $\bf{S}$ are togrther, is $\displaystyle = \binom{5}{3}\times \frac{4!}{2!} = 120$

Now I did understand How can i Calculate after that

Thanks

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
Now Total no. of words in which no two $\bf{S}$ are togrther, is $\displaystyle = \binom{5}{3}\times \frac{4!}{2!} = 120$
Subtract from that the number of words where no two S's are together, but both C's are together.

#### jacks

##### Well-known member
Total no. of words in which two $\bf{S}$ are not together and two $\bf{C}$ are together
$\displaystyle = \binom{4}{3}\times 3! = 24$
Now Total no. of words in which no two $\bf{C}$ and no two $\bf{S}$ are together , is $= 120-24 = 96$