1. How many three digit even numbers can be formed from the digits 1, 2, 3, 4, 5

Question

1. How many three digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if no repetitions are allowed?

2. In how many ways can 3 English, 3 Math, and 4 Spanish books be set on a shelf if the books are grouped by subject?

3.On a soccer team three fullbacks can play any of the three fullback positions, left, center, and right. The three halfbacks can play any of the three halfback positions, the four forwards can play any of the four positions, and the goalkeeper plays only his position. How many different arrangements of the 11 players are possible?

Explanation / Answer

1)

Even: It has to end in 2 or 4. There aretwo possible values for the last digit.
The first digit can be anything . We have 4 options for first digit.
For last digit we will have 3 options.

So answer would be 4*3*2 = 24

2) 3!*3!*4!*3!

English,Math, and Spanish books can be set on a shelf if the books are grouped by subject in 3! ways

Now within english books number of possible combination is 3!

similarily within math books number of possible combination is 3!

similarily within spanish books number of possible combination is 4!

So answer would be 3!*3!*3!*4! = 5184

3) Similar to above reasoning different arrangements possible are 3!*3!*4!*1 = 864

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