more permutations

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
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.


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


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.....