Counting

Counting > With or without repeating

Overview

1234With or without repeating

Solutions to the exercises

Exercise 1

$10^{4} \cdot 26^{2} = 6760000$

Exercise 2

$2^{35}$

Exercise 3

$15 \cdot 14 \cdot 13 = 2730$

Exercise 4

$8! = 40320$ possibilities.

Seat this person first. You can do that at either end of the row. The other seven can be seated in a random order.

$2 \cdot 7! = 10080$ possiblities.

This couple can sit in $7$ places. For the others there are $6$ places left. But the couple can exchange places! So $2 \cdot$ 7 $\cdot 6! =$ 10080 possibilities.

Exercise 5

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