Count using the addition and$/$or multiplication rule

Count using binomial coefficients

How many $7-$bit strings begin with $1011$ and end with $1100?$

How many $7-$bit strings begin with $11$ or $0011?$

Compute and interpret the number of combinations and$/$or permutations

How many $7$ digit numbers contain exactly three $1$ s and four $2s?$

Count using 'stars and bars

How many ways can you hide $5$ gift certificates under $24$ seats for an upcoming event?

Count using the principle of inclusion$/$exclusion $($PIE$)$

Eight guests bring a gift and each receives another gift in return. No one is allowed to receive the gift they brought. How many ways are there to distribute the gifts? $($Hint: think derangements$)$