(a) A bank’s safe has 5 dials each of which can be set to anumber 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 tothe same number?
iii. How many possible settings are there if all the numbersmust be even (count 0 as even), and duplicate numbers arepermitted?
iv. Re-do the previous question, but this time with noduplicates allowed.
(b) Suppose the bank gets a new safe also with 5 dials, but eachdial is numbered as follows: Dial 1 goes from 0 to 10 Dial 2 goesfrom 0 to 12 Dial 3 goes from 0 to 20 Dial 4 goes from 0 to 25 Dial5 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 tothe same number?
iii. How many possible settings are there if all the numbersmust be even (count 0 as even), and duplicate numbers arepermitted?
iv. Re-do the previous question, but this time with noduplicates allowed.
