f.5 permutation and combinatio

1. By choosing 4 different numerals from the ten numerals 0 to 9, how many 4-digit numbers that are divisible by 5 can be formed? (ans: 952)

2. by using 10 cards marked 0 to 9 respectively, how many 5-digit numbers that are not divisible by 10 can be formed? (ans:24192)

3. there are 11 books on a shelf in a library. 3 of them are the same and 2 others are also the same. how many ways of arranging the books are there if the same books are placed together?(ans: 40320)

4. on a table there are 12 balls of different colours. if 6 of the balls are put into a bag and one particular ball must be selected, how many combinations of balls are there?(ans:462)

5. a pack of 52 playing cards is divided into four suits: spades, hearts, clubs and diamonds. the number of cards in each suit are the same. how many combinations of 4 cards from the pack are possible if at least one heart is taken?(ans:188474)