Consider all the $5$ digit numbers where each of the digits is chosen from the set $\{1,2,3,4\}$. Then the number of numbers which contain all the $4$ digits is?
I don't know where to start. Would love some help/hints.
2026-03-29 17:24:48.1774805088
Number of numbers - P&C
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HINT:
Since there are just 4 numbers, and 5 digits and you want all of them to be present, you'll have to take care only of a few things. Note that you'll have to pick only one extra digit. In how many ways can you do that? After choosing that digit, in how many ways can you arrange them?
SOLUTION:
Ways to choose extra digit$=4$
Ways to arrange them$=5!/2$
Answer = Total combinations$=2*5!$