COMEDK · Maths · 4. Permutation Combination
In how many ways can the squares of a \(4 \times 2\) grid (4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?
- A \(17280\)
- B \(10080\)
- C \(9360\)
- D \(8640\)
Answer & Solution
Correct Answer
(D) \(8640\)
Step-by-step Solution
Detailed explanation
The word 'SPHERE' consists of 6 letters, in which 'E' appears twice and the rest are distinct. The given grid has 4 rows and 2 columns, making a total of 8 squares. Since there are 6 letters to be placed in 8 squares, exactly 2 squares will remain empty. The condition states…
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