# more permutations

#### xo_caroline_xo

##### New Member
find the number of ways of arranging the letters of MATCHING if;
a. there are no restrictions;
b. the first letter must be M;
c. the odd numbered positions must remain unchanged;
d. the arrangement must end with NG

caroline xoxo

#### galactus

##### New Member
This is just a matter of arrangements.

a. There are 8 letters in the owrd MATCHING, therefore, 8! ways of arranging it.

b. If the first letter is M, then set it in place and arrange the other 7.

#### xo_caroline_xo

##### New Member
so for part d, would you do 8!/6! * 2?

#### JohnM

##### TS Contributor
a. here, there are no restrictions on where letters can go, so you start with:

xxxxxxxx

there are 8 slots for the first letter, 7 for the second, and so on, so it's 8! (factorial)

b. Mxxxxxxx

there are 7 slots for the first letter, 6 for the second, etc. --> 7!

c. MxTxHxNx

same exact idea as a. and b., but you start with 4 slots

d. xxxxxxNG

starting with 6 slots.....