Quantity B: How many words having 3 consonants and 2 vowels can be for

1.	Quantity B: How many words having 3 consonants and 2 vowels can be formed out of 5 consonants and 4 vowels?1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B
Answer» Quantity A: One book for bookshelf 1 can be selected in ⁷C₁ ways. Two books for bookshelf 2 can be selected in ⁶C₂ ways. REMAINING books = 4 and Remaining bookshelves = 3. Out of these 4 books, 1^st book can be PUT in any of these 3 bookshelves. Similarly 2^nd book can be put in any of these 3 bookshelves. 3^rd book can be put in any of these 3 bookshelves. 4^th book can be put in any of these 3 bookshelves. ∴ These 4 books can be arranged in 3 × 3 × 3 × 3 = 81 ways ∴ Required number of ways = ⁷C₁ × ⁶C₂ × 81 =7 × 15 × 81 = 8505 Quantity B: Number of ways to choose 3 consonants and 2 vowels out of 5 consonants and 4 vowels = ⁵C₃ × ⁴C₂ = 10 × 6 = 60 Number of ways in which 5 LETTERS can be arranged = 5! = 120 ∴ Required number of words = 60 × 120 = 7200 ∴ Quantity A > Quantity B

Quantity B: How many words having 3 consonants and 2 vowels can be formed out of 5 consonants and 4 vowels?1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Quantity A:

One book for bookshelf 1 can be selected in ⁷C₁ ways.

Two books for bookshelf 2 can be selected in ⁶C₂ ways.

REMAINING books = 4 and Remaining bookshelves = 3.

Out of these 4 books, 1^st book can be PUT in any of these 3 bookshelves.

Similarly 2^nd book can be put in any of these 3 bookshelves.

3^rd book can be put in any of these 3 bookshelves.

4^th book can be put in any of these 3 bookshelves.

∴ These 4 books can be arranged in 3 × 3 × 3 × 3 = 81 ways

∴ Required number of ways

= ⁷C₁ × ⁶C₂ × 81

=7 × 15 × 81 = 8505

Quantity B:

Number of ways to choose 3 consonants and 2 vowels out of 5 consonants and 4 vowels

= ⁵C₃ × ⁴C₂ = 10 × 6 = 60

Number of ways in which 5 LETTERS can be arranged = 5! = 120

∴ Required number of words = 60 × 120 = 7200

∴ Quantity A > Quantity B