Multiple Choice Exercise

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1.1 What is the number of cases in which four students sit at a round table?

1
2
24
6

        

1.2 Using 10 numbers 0,1,2,..., 9, in how many cases can you create a four-digit password by allowing duplicates?

1000
10000
264256
21474838

        

1.3 In how many cases can the letters in the word 'mathematics' be arranged in a row?

1663200
4989600
415800
34650

        

1.4 A vacuum tube can be represented by the numbers 1 and 0 for electricity coming in and going out. What is the number of cases that can be represented by a bundle of 8 vacuum tubes.

8
128
256
512

        

1.5 What is the coefficient of \(a^2 b^4\) in the expansion of \((a+b)^6\)?

15
20
6
1