Question 1: Committee Formation with Minimum Men Condition
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?
Question 2: Word Arrangement with Vowels Together
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Question 3: Word Formation with Specific Vowel-Consonant Pattern
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Question 4: Word Arrangement with Repeated Letters
In how many ways can the letters of the word 'LEADER' be arranged?
Question 5: Children Selection with Minimum Boy Condition
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?
Question 6: 3-Digit Numbers with Specific Conditions
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Question 7: Committee Formation from Men and Women
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Question 8: Ball Selection with Minimum Condition
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
Question 9: Word Arrangement with Vowels in Specific Positions
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?
Question 10: Word Arrangement with Consonants Together
In how many different ways can the letters of the word 'EDUCATION' be arranged in such a way that the consonants always come together?