Test: Probability I - Challenging

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Question 1:   A student has 8 math books, 4 English books and 5 history books. In how many ways can this student put the books on the shelf so that books of the same subject would stand together?
4!×5!×8! ÷3!
160 3
4!×5!×8! ×3!
480
Question 2:   Five girls and five boys are sitting down on 10 chairs one after one. In how many ways they can sit so that boys would sit on the chairs with even numbers and girls - in the chairs with odd numbers?
5! 2
5! 2 ×10!×2!
25
10!
Question 3:   In how many ways can the orders of printing 9 different books be distributed to 2 factories?
18
9 2
2 9
2!×9!
Question 4:   There are 32 students in a classroom. Each second student exchanged a pen for another one. How many times pens were exchanged?
16
64
992
32!
Question 5:   How many different six-digit numbers can be formed out of 1,2,3,4,5,6,7 ?  Digits should not repeat and only even digits should be at the beginning and the end of a number.
5040
720
42
15
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