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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 diff ways are there for the student to choose sandwiches for the 7 days of a week if the order in which sandwiches are chosen matters
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$6^{7} ?$

On the first day, the student can choose any $1$ of the available $6$ kinds of sandwiches, so total number of ways to choose a sandwich on first day will be $^6C_1=6$. Similarly, the student will have $6$ choices on each of the next $6$ days, hence total number of ways to choose sandwiches for the $7$ days of week will be:
$6*6*6*6*6*6*6$
$=6^7$
$=279936$