We have 10 numbers from 0 to 9. When no digit is repeated, so we get 10! ways that is = $10\times9\times8\times7\times6\times5\times4\times3\times2\times1$

= 3628800

b) How many social security cards that can be issued with at least one digit repeated?

We will get this by subtracting 10! from all possible cases.

$10^{9}-10!$

= $1000000000-3628800=996371200$

Exercise 4.

a) How many nonempty subsets are in a set of 5 elements?

Each element has 2 choices that are either selected in subset or not selected in subset.

Here, total choices will be $2^{5}$

And it is 1 time that no element is selected.

So, the number of non empty subsets will be = $2^{5}-1$

=> $32-1=31$

b) Erika has 5 friends. In how many ways can she invite one or more friends to a dinner party?

Same like above part, here Erika has two choices for each friend, either invite or not invite.

So, she has total $2^{5}=32$ choices.

1 way to not invite anyone.

Hence, the number of ways can she invite one or more friends to a dinner party = $32-1=31$ ways.

8 0

3 years ago

Two numbers have the same digit in the millions. The same digits in a thousand. In the in the same digit in the ones. Do these t

Blababa [14]

No it does not have the same value

7 0

3 years ago

Read 2 more answers