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PROBABILITY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPROBABILITY1 Mark
MCQ
Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is:
  • ✓
    $\frac{\ ^{7}\text{P}_5}{7^5}$
  • B
    $\frac{\ ^{7^5}}{\ ^{7}\text{P}_5}$
  • C
    $\frac{\ ^{6}}{\ ^{6}\text{P}_5}$
  • D
    $\frac{\ ^{5}\text{P}_5}{5^5}$
✓

Answer

Correct option: A.
$\frac{\ ^{7}\text{P}_5}{7^5}$
  1. $\frac{\ ^{7}\text{P}_5}{7^5}$​
Solution:
Since, it is an eight - storey building.
So, there are 7 possible options for them in 7 floors in total if ground floor is not considered.
Hence, total possible outcomes = $7 \times 7 \times 7 \times 7 \times 7=7^5$
Thus, number of ways in which 5 persons can leave from seven floors differently $=\ ^{7}\text{P}_5$
Required probability $=\frac{\ ^{7}\text{P}_5}{7^5}$

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