Permutations & Combinations Question - None

Question

In how many ways can the letters of the word DIPESH be placed in the squares of the adjoining figure so that no row remains empty?

Accepted Answer

Step 1: The word DIPESH has 6 letters. There are 8 squares in the figure arranged in rows.

Step 2: We need to select 6 squares from 8 to place the letters such that no row remains empty.

Step 3: Total ways to select 6 squares from 8: $$\binom{8}{6} = \binom{8}{2} = \frac{8 \cdot 7}{2} = 28$$

Step 4: Exclude cases where either the top row or bottom row has no X (letter):

Cases to exclude = 2 (either top row empty or bottom row empty)

Step 5: Required number of ways = 28 - 2 = 26

Question: