Question

Total number of ways of selecting five letters from the word 'POLYGON' is?​

Answer 1

Answer:

POLYGON

In selected five letters

Answer 2

What is the total number of ways of selecting five letters from the word polygon?

Polygon is a seven letter word; which has two Os, one P, one L, one G, one Y and one N.

Five letters to be chosen.

There can be two patterns of choosing.

Pattern-1: Choosing two Os and three other letters. It can be done in {(2C2) * (5C3)} = (1 * 10) = 10 ways.

Pattern-2: Choosing one O and four other letters. It can be done in {(2C1) * (5C4)} = (2 * 5) = 10 ways.

Combining the two patterns above, there are (10 + 10) = 20 ways of selecting five letters.