5 numbers are to be chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} How many ways can 5 (not necesarilly distinct) numbers be chosen?

How many ways are there in choosing (55+1) face mask  from a box of  (55+3) face masks?

A 4-digit number is selected from the numbers {1,2,3,4,5,6}{1,2,3,4,5,6} where the digits are selected without replacement. How many 4-digit numbers can be selected that are greater than 4000? How many even 4-digit numbers can be chosen? How many 4-digit numbers can be chosen that are even and greater than 4000?

How many 4-digit numbers are there that are divisible by 10 and the sum of whose digits is 10?

Seven prizes are to be given to seven different people in a group of nineteen. In how many ways can a first prize, a second prize, a third prize and four fourth prizes be given?