The number of ways in which 4 vowels and 2 consonants be chosen from equation is
Question 1. How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?Solution: Show
Question 2. How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?Solution:
Question 3. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?Solution:
Question 4. If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?Solution:
Question 5. How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7, and 9 which are divisible by 10, and no digit is repeated?Solution:
Question 6. The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?Solution:
Question 7. In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?Solution:
Question 8. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.Solution:
Question 9. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?Solution:
Question 10. From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?Solution:
Question 11. In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?Solution:
How many words of 3 consonants and 2 vowels can be formed?Number of groups, each having 3 consonants and 2 vowels =210.
How many words consisting of four consonants and 2 vowels can be formed out of 6 consonants and 4 vowels?Required number of ways = (210 x 120) = 25200.
How many words of 3 consonants and 3 vowels can be formed from 8 consonants and 4 vowels?∴ The required result will be 40320.
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