Answer to Question #278084 in Discrete Mathematics for Himanshi

Question

How many numbers can be formed using the digits 1, 3, 4, 5, 6, 8 and 9 if no

repetition is allowed?

13) Suppose that we draw a card from a deck of 52 cards and replace it before the

next draw. In how many ways can 10 cards be drawn so that the tenth card is a

repetition of a previous draw?

Answer 1

Since there are 7 digits so numbers formed without repetition is $7!=5040$

13)

The first card can be drawn in 52 different ways. The next card can be drawn in 51 different ways and the next in 50 different ways. So, the number ways ten cards can be drawn without replacement is $52\times51\times50\times49\times48\times47\times46\times45\times44\times43=5.74\times10^{16}$