# (a) A bank’s safe has 5 dials each of which can be set to a number...

(a) A bank’s safe has 5 dials each of which can be set to a number from 0 to 36 (so each dial has 37 possible settings).

i. How many different ways can the 5 dials be set?

ii. How many settings are there if no two dials may be set to the same number?

iii. How many possible settings are there if all the numbers must be even (count 0 as even), and duplicate numbers are permitted?

iv. Re-do the previous question, but this time with no duplicates allowed.

(b) Suppose the bank gets a new safe also with 5 dials, but each dial is numbered as follows: Dial 1 goes from 0 to 10 Dial 2 goes from 0 to 12 Dial 3 goes from 0 to 20 Dial 4 goes from 0 to 25 Dial 5 goes from 0 to 35

i. How many different ways can the 5 dials be set?

ii. How many settings are there if no two dials may be set to the same number?

iii. How many possible settings are there if all the numbers must be even (count 0 as even), and duplicate numbers are permitted?

iv. Re-do the previous question, but this time with no duplicates allowed.

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