Please help!Permutations?

In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time?

In how many different ways can you arrange the letters of the word TRIGONOMETRY?

In how many different ways can the 9 starters of a baseball team be placed in their positions?

How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)?

Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule?

How many seven-digit phone numbers can be formed if the first digit cannot be 0 and

repetition of digits is not permitted?

if repetition of digits is permitted?

The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?

Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:

the first letter must be Y

the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first).

Here's a hint: don't put your whole homework assignment in one question...nobody wants to do you homework for you.

You'll have better luck if you ask one question at a time. That way, you'll appear as though you actually want to learn the concepts and processes, rather than just obtain the answers.