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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals
  • A
    $\frac{1}{2}$
  • ✓
    $\frac{7}{15}$
  • C
    $\frac{2}{15}$
  • D
    $\frac{1}{3}$
✓

Answer

Correct option: B.
$\frac{7}{15}$
(B)
The number of ways to arrange 7 white and 3 black balls in a row $=\frac{10!}{7!\cdot 3!}=\frac{10.9 .8}{1 \cdot 2.3}=120$
Numbers of blank places between 7 balls are 6. There is 1 place before first ball and 1 place after last ball. Hence, total number of places are 8.
Hence, 3 black balls are arranged on these 8 places so that no two black balls are together in number of ways
$={ }^8 C_3=\frac{8 \times 7 \times 6}{1 \times 2 \times 3}=56$
So required probability $=\frac{56}{120}=\frac{7}{15}$.

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