Question

A box contains 8 blue and 6 red socks . What is the number of ways that 2 socks can be drawn from the box such that they have same colour​

Answer 1

Above it's is explained, that we used combination.

Answer 2

The number of ways that 2 socks can be drawn from the box such that they have same colour is 43 ways.

Given: A box contains 8 blue and 6 red socks.

To find: The number of ways that 2 socks can be drawn from the box such that they have same colour.

Solution:

We know the combination formula is:  nCr += n! / r! × (n-r)!

Where, 'nCr' is the number of required combinations, 'n' is the total number of objects in the set and 'r' is the number of choosing objects from the set.

∴ The total number of ways that we can select 2 socks that have same colour = 8C2 + 6C2

= [(8×7×6!) / 2! × (8-2)!] + [(6×5×4!) / 2! × (6-2)!]

= [(8×7×6!) / (2! × 6!)] + [(6×5×4!) / (2! × 4!)]

= 56/2 + 30/2

= 28 + 15

= 43

Therefore, the number of ways that 2 socks can be drawn from the box such that they have same colour is 43 ways.

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