Question

HELP ASAP!!! PLEASE SHOW SOLUTIONS!!​

Answer 1

1. 84 ways
2. 3,780 numbers
3. 3,628,800 ways

Explanation:

Solving :

Q1

• No. of ways to choose 6 from 9 :
• ⁹C₆ = 9! / 6! 3!
• 9 x 8 x 7 x 6! / 6! x 3 x 2
• 3 x 4 x 7
• 28 x 3
• 84 ways

Q2

• No. of numbers with distinguishable digits :
• 9! / 4! 2! 2!
• 9 x 8 x 7 x 6 x 5 x 4! / 4! x 2 x 2
• 9 x 2 x 7 x 6 x 5
• 10 x 63 x 6
• 378 x 10
• 3,780 numbers

Q3

• No. of ways to arrange :
• 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
• 90 x 56 x 30 x 24
• 5040 x 720
• 3,628,800 ways