Question

Every day a student randomly chooses a sandwich for lunch from a pile of wrapped sandwiches. If there are six kinds of sandwiches, how many different ways are there for the student to choose sandwiches for the seven days of a week if the order in which the sandwiches are chosen matters?

Answer 1

Answer:

279,936 ways

Step-by-step explanation:

Every day the student has to chose a sandwich from the pile of 6 sandwiches.  So this means the student has to make a choice from the 6 sandwiches for the 7 days. Since the order matters, this is a problem of permutations.

Daily the student has the option to chose from 6 sandwiches. So this means, for 7 days, he has to make a choice out of 6 options. Or in other words we can say, the student has to make selection from 6 objects 7 times.

So, the total number of ways to chose the sandwiches will be 6 x 6 x 6 x 6 x 6 x 6 x 6 = $6^{7}$

Alternate Method:

Since the repetition can occur in this case, i.e. a sandwich chosen on one day can also be chosen on other day, the following formula of permutations ca be used:

Number of ways =  $n^{r}$

where n is the total number of choices available which is 6 in this case and r is the number of times the selection is to be made which 7 in this case. So,

The number of ways to chose a sandwich will be = $6^{7} = 279936$ ways