Multiple choice

The number of ways in which six '+' and four '–' signs can be arranged in a line such that no two '–' signs occur together is

  1. 30

  2. 35

  3. 6!5!

  4. 6!2!

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arrange 6 '+' signs: _ + _ + _ + _ + _ + _ _. There are 7 gaps. We need to place 4 '-' signs in these 7 gaps such that no two are together. This is 7C4 = 35 ways.

AI explanation

To ensure no two minus signs are together, first arrange the six plus signs in a single row. This creates seven available gaps (five between adjacent plus signs, plus the two ends). Select four of these seven gaps to place the minus signs using the combination formula nCr, giving 7C4 = 35. The required number of arrangements is 35.

Keep practicing — related questions