Using permutation formulas,?

In how many different ways can 6 classes be scheduled during a 6-period day?
In how many different ways can you arrange the letters of the word INTERNET?
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?
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?

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In how many different ways can 6 classes be scheduled during a 6-period day?
There are 6!=720 ways.

In how many different ways can you arrange the letters of the word INTERNET?
There are 8!/(2!2!2!)=5040 ways.

In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time?
There are 8P4=8!/4!=1680 ways.

In how many different ways can you arrange the letters of the word TRIGONOMETRY?
There are 12!/(2!2!2!)=12!/8 ways.

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

How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)?
There are 4*4=16 ways.

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?
There are 10C6=10!/(4!6!)=210 ways.

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?
There are 12!/12=11! ways.