Question

There are 3 white and 5 pink flowers in a box. In how many ways can

(1 ) three flowers of same colour be selected?

(2) 2 flowers of different colours be selected?

Answer 1

In a box there are 3 white and 5 pink flowers.

(1) Selected three flowers are of the same colour:

3 whIte flowers of 3 white flowers can be selected in ³C₃ ways or

3 pink flowers of 6 pink flowers can be selected in ⁶C₃ ways.

∴ Total combinations = ³C₃ + ⁵C₃

= 1 + \(\frac{5×4×3}{3×2×1}\)

= 1 + 10 = 11

(2) Selected two flowers are of different colours:

1 white flowers out of 3 whIte flowers can be selected in ³C₁ ways and

1 pink flower out of 5 pink flowers can be selected In ⁵C₁ ways.

∴ Total combinations = ¹C₁ × ⁸C₃

= 3 × 5

= 15