Probability - Arithmetic Aptitude Questions and Answers

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In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

$\frac { 21 } { 46 }$

$\frac { 25 } { 117 }$

$\frac { 1 } { 50}$

$\frac { 3 } { 25 }$

Answer : Option A

Explanation :

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S)	= Number ways of selecting 3 students out of 25
	= ²⁵C₃

= $\frac { (25*24*23) } { (3*2*1) }$

=2300

n(E)	= (¹⁰C₁ x ¹⁵C₂)

= [ 10 X $\frac { (15*14) } { (2*1) }]$

=1050

P(E) = $\frac {n(E) } { n(S) }$ = $\frac { 1050 } { 2300 }$ = $\frac { 21 } { 46 }$

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