Question

You eat five days per week at the same restaurant, and every day you order a sandwich and a drink. There are 20 sandwiches including 6 vegetarian options, and 14 drinks including 4 caffeine-free drinks. On Tuesdays, you like to eat healthy, so you always choose a vegetarian sandwich and a caffeine free drink on Tuesdays. The other days you can eat any sandwich and drink any drink - but you never repeat a sandwich or a drink in the same 5-day week. How many different 5-day meal plans fit your rules?

Answer 1

Number of Sandwich options = 20

Number of drink options = 14

Number of vegetarian sandwich options = 6

Number of caffeine-free drinks = 4

Tuesday :  always choose a vegetarian sandwich and a caffeine free drink

Number of different plan meals for Tuesday = Number of vegetarian sandwich options x Number of caffeine-free drinks = 6 x 4 =24

For remaining 4 - days :

Since you have already opted for  one of the vegetarian sandwich ; Remaining options in sandwiches = 20-1=19

and

Since you have already opted for  one of the of caffeine-free drinks  ; Remaining options in drinks = 14-1=13

Without repetitions,

Number of ways choosing 4 sandwiches(for 4 days) from 19 sandwich options =

Number of ways choosing 4 drinks (for 4 days) from 13 drink options =

Number of different plan meals for 4-days(5-week day- Tues day) = = 2771340

Number of different 5-day meal plan

= Number of different plan meals for 4-days(5-week day- Tues day) x Number of different plan meals for Tuesday

=2771340 x 24 = 66512160

Number of different 5-day meal plan = 66512160