Find the number of ways in which 10 different diamonds can be arranged to make a necklace.

Find the number of ways in which 8 different flowered can be strung to form a garland so that four particular flowers are never separated.

Find the number of ways in which n different prizes can be distributed among m(< n) persons if each is entitled to receive at most n-1 prizes.

There are six periods in each working day of a school. Find the number of ways in which 5 subjects can be arranged if each subject is allowed at least one period and no period remains vacant.

Find the number of ways in which 22 different books can be given to 5 students, so that two students get 5 books each and all the remaining students get 4 books each.

Find the number of ways in which 5 girls and 5 boys can be arranged in row (i) if no two boys are together. (ii) if boys and girls are alternate. (iii) all the girls sit together and all the boys sit together. (iv) all the girls are never together.

Find the number of ways in which 16 constables can be assigned to patrol villages, 2 for each.

Find the number of ways in which 5A^(prime)sa n d6B ' s can be arranged in a row which reads the same backwards and forwards.

Find the number of ways in which six persons can be seated at a round table, so that all shall not have the same neighbours n any two arrangements.

Out of 8 sailors on a boat, 3 can work only on one particular side and 2 only on the other side. Find the number of ways in which the sailors can be arranged on the boat.

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color.