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01.  In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?  

02.  In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?  

03.  In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  

04.  From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?  

05.  Find the number of ways in which a group of 4 boys and 3 girls can be selected out of a total of 9 boys and 9 girls.  

06.  Find the number of ways in which 4 cattle can be selected from a group of 9 cows and 5 buffaloes, such that there is at least 1 buffalo present.  

07.  The number of ways of forming a committee of 6 members from a group of 4 men and 6 women is  

08.  The number of rectangles that can be formed on a 8 Ã— 8 chessboard is  

09.  The number of distinct lines that can be formed by joining 20 points on a plane is of which no three points are collinear is  

10.  Find the number of ways of studding 10 beads to form a necklace  
