MATHS & STAT問題

因為我自修maths & stat,所以連這般簡單的也不懂
希望各位學過maths & stat的朋友可以以mathS & stat的角度解釋一下
唔該晒~
2. A child has 6 sweaters and 7 pairs of trousers. How many different outfits can he/she wear?
The number of different outfits =

5. A student must take a social science subject and a language subject. The social science
subjects available are Economics, Geography and Commerce. The language subjects
available are English, Chinese, Japanese, German and French. How many ways can the
student arrange his/her study program?
The number of ways =

7. A computer shop has 5 types of monitors, 4 CPU systems and 7 printers available. How
many different computer systems consisting of a monitor, a CPU system and a printer can
be formed?
The number of different computer systems =

9. A four-course dinner consists of a soup, a main dish, a dessert and a drink. If one can
select from 4 different soups, 5 main dishes, 3 desserts and 6 drinks, how many dinner
choices are possible?
The number of dinner choices =

11. There is a 6-digit Personal Identification Number (PIN) encoded in each bank card for
security reasons. Find the number of possible PINs
(a) with repeated digits allowed,
The number of possible PINs =
(b) with no repeated digits.
The number of possible PINs =

18. A vehicle licence plate consists of 2 letters followed by 4 digits.
(a) How many different plates are possible with no restriction?
The number of different plates =
(b) How many different plates are possible if the letters O and I are excluded?
The number of different plates =
(c) How many different plates are possible if the letters O and I are excluded and at
least one of the digits is 8?
If the digit 8 is excluded, the number of different plates =
∴ The required number =