Answer to Question #113285 in Combinatorics | Number Theory for Saketh

Question

On Sunday either go to the cinema or to the theatre, on each Monday, Tuesday and Wednesday you can study either maths, physics or chemistry, on each of Thursday, Friday and Saturday you can visit one of your 5 best friends (you must choose exactly one thing for each day).
In how many different ways can you plan your week?

Answer 1

Solution.

On Sunday: there are two different ways to choose;

on Monday: there are three different choices;

on Tuesday :there are three different choices;

on Wednesday :there are three different choices;

on Thursday: five different choices;

on Friday: five different choices;

on Saturday: five different choices.

The number of ways to plan your week is: $2\sdot3\sdot3\sdot3\sdot5\sdot5\sdot5 = 6750;$

Answer: There are 6750 ways to plan a week.