Please provide the formal and your final answer. $($for example, permutation: $5!=$

$120)(10$ points for each question except Q$4)$

$1.$ How many ways can $7$ floats line up for the homecoming parade?

$2.$ How many ways can $4$ of $7$ different kinds of bushes be planted along a

walkway?

$3.$ How many ways can you choose three people to be secretary$,$ vice president,

and president in a club of $25$ people?

$4.$ A committee of $8$ students is to be selected from a class consisting of $19$

freshmen and $34$ sophomores. $(20$ points$)$

a$.$ In how many ways can $3$ freshmen and $5$ sophomores be selected?

b$.$ In how many ways can a committee with exactly $1$ freshman be

selected?

c$.$ In how many ways can a committee with at most $1$ freshman be

selected?

d$.$ In how many ways can a committee with at least $1$ freshman be

selected?

$5.$ If you have $4$ pairs of pants, $8$ shirts, and $5$ hats, how many ways can you

choose your outfit?

$6.$ How many three digits numbers $(100-999)$ are evenly divisible by $5?$

$7.$ How many three digits numbers $(100-999)$ are not evenly divisible by $5?$

$8.$ There are $10$ fish left at the local aquarium supply store, but your pond at

home can only hold three fish. How many different collections of fish can live

in your pond?

$9.$ You have six identical puppies that need to be adopted. Assuming that three

families arrive looking to adopt dogs, how many ways could the puppies be

distributed to the families for adoption?