Question

five marbles are drawn from a bag which contain 7 blue marbles and 4 black marbles what is the probability that all will be blue​

Answer 1

The probability that all will be blue​ is  $\dfrac{1}{22}$.

Explanation:

Given : Number of blue marbles = 7

Number of black balls =4

Total balls = 11

Number of combinations of taking 5 marbles out of 11 = $^{11}C_5$

Number of combinations of taking 5 marbles out of 7 blue marbles = $^7C_5$

The probability that all will be blue​ = $\dfrac{^7C_5}{^{11}C _5}$

Since , $^nC_r=\dfrac{n!}{r!(n-r)!}$

Then, The probability that all will be blue​ =$\dfrac{\dfrac{7!}{5!2!}}{\dfrac{11!}{5!6!}}=\dfrac{1}{22}$

Hence, the probability that all will be blue​ is  $\dfrac{1}{22}$.

# Learn more :

A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of not drawing a black marble is . The probability of drawing a red marble is

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