Varsha is making different styles of colour pattern by drawing 5 vertical lines from left to right. She has decided to draw 3 vertical lines with crayon
colours and 2 vertical lines with water colours. She has 3 different water colours and 2 different crayon colours (all 5 colours are distinct) at her
disposal How many different patterns can she create using these colours if repetition of colours is allowed? (The page on which vertical stripes are
made is not rotated while making or observing later)
Answers
Given : Varsha is making different styles of colour pattern by drawing 5 vertical lines from left to right.
She has decided to draw 3 vertical lines with crayon colours and 2 vertical lines with water colours. She has 3 different water colours and 2 different crayon colours (all 5 colours are distinct) at her disposal
To Find : different patterns she can create using these colours if repetition of colours is allowed
Solution:
3 lines with crayon
2 lines with water colors
Total Lines = 5
3 lines out of 5 can be selected in ⁵C₃ = 10 way
Hence 10 ways of selecting lines
Now each water color line can be colored in 3 * 3 = 9 ways
each crayon color line can be done in 2 ways Hence 3 lines can be in
2 * 2 * 2 = 8 ways
Total Ways = 10 * 9 * 8 = 720 ways
720 different patterns can be created,
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