Question no 137 SSC CGL Tier 1 Quantitative Aptitude Questions and Answers Online Test 2

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1 .

The letters of the word SOCIETY are placed at random in a row. The probability that the three vowels come together is
A.$1\over6$ , B.$1\over7$ , C.$2\over7$, D.$5\over6$

[ A ] a
[ B ] b
[ C ] c
[ D ] d

Answer : Option B

Explanation :

The word ‘SOCIETY’ contains seven distinct letters and they can be arranged at random in a row in $^7p_7$ ways, i.e. in 7! = 5040 ways
Let us now consider those arrangements in which all the three vowels come together. So in this case we have to arrange four letters. S,C,T,Y and a pack of three vowels in a row which can be done in $^5p_5$ i.e. 5! = 120 ways.
Also, the three vowels in their pack can be arranged in $^3p_3$ i.e. 3! = 6 ways.
Hence, the number of arrangements in which the three vowels come together is 120 × 6 = 720
∴ The probability that the vowels come together =
$720\over5040$=$1\over7$

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