Permutations and Combinations Exam Pattern Mix

A box holds 5 different red balls and 3 different white balls. In how many ways can 4 balls be chosen with at least one of each colour?

How many different bracelets can be made from 6 beads of different colours?

A host sits in a fixed chair at the head of a round table for 8. His 7 guests take the other seats, but the guest of honour must sit on the host's right. In how many ways?

4 different maths books and 3 different English books go on a shelf with all the English books together. In how many ways?

4 different maths books and 3 different English books are arranged so that no two English books are side by side. In how many ways?

A team of 3 is chosen from 4 boys and 3 girls with at least one girl. In how many ways?

In how many ways can the letters of REGULATION be arranged so that the vowels occupy only the even positions?

How many arrangements of the letters of REGULATION begin with R and end with N?

In how many ways can 3 different numbers be chosen from 1 to 20 so that their sum is even?

In how many ways can 5 identical chocolates be shared among 3 children if some may get none?