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Question

Three numbers are chosen at random without replacement from {1,2,3,,10}. The probability that, the smallest of the chosen number is 3 or the greatest one is 7, is equal to

A
740
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B
1140
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C
940
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D
1340
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Solution

The correct option is B 1140
Let E1 be the event:
getting the smallest number 3 and
E2 be the event:
getting the greatest number 7
Then, P(E1)=P (getting one number 3 and other two from 4 to 10)
=1C1×7C210C3=740
Similarly, P(E2)=P(getting one number 7 and other two number from 1 to 6)
=1C1×6C210C3=18
P(E1E2)=P(getting one number 3 and second number 7 and third number from 4 to 6)
=1C1×1C1×3C110C3=140
P(E1E2)=P(E1)+P(E2)P(E1E2)
=740+18140=7+5140=1140

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