Three numbers are chosen at random without replacement from 1 to 10. The probability that the minimum of the chosen number is 3, and their maximum is 7, is?

Question

Jayant Kishore · Answer

Number of elements in sample space = 10 C 3 =120 According to the question 3 & 7 must get chosen and the third no. should be between them (ie 4 or5 or 6)as per condition . So, no of favourable cases = 3 C 1 =3 Therefore required probablity = 3/120 = 1/40 Approve the answer if correct .

Jayant Kishore · Answer

Alternatively , you can proceed this way. No. of elements in sample space = 10 x 9 x 8 for selection of 3 numbers one by one without replacement. According to the question 3 & 7 must get chosen and the third no. should be between them (ie 4 or5 or 6) as per condition . So , favourable selection may be as 3 , 7 , X where X denotes either of 4 or 5 or 6. This can be done in 3 ways. But , here since we are selecting one by one , IN THIS CASE ORDER OF SELECTION MATTERS So, no of favourable cases = 3! x 3 Therefore required probablity = 3! x 3/ (10 x 9 x 8) = 1/40. NOTICE THE DIFFERENCE .

Humanshu Parkhade · Answer

P(min 3 union max 7)= p(min 3)+ p(max 7) - p( min3 intersection max7). Now put the values........... 8C3 by 10C3. +7C3 by 10C3 -5C3 by 10C3 .... Solve this u get answer correctlt

Kushagra Madhukar · Answer

Dear student, Please find the attached answer to your question. Number of ways in which 3 random numbers can be drawn from 1 to 10 = 10 C 3 = 120 It is given that 3 & 7 must get chosen and the third no. should lie between them Therefore, the possible third number can be either of 4, 5 or 6 So, favourable cases = 3 C 1 = 3 Therefore required probablity = 3/120 = 1/40 Hope it helps. Thanks and regards, Kushagra

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Three numbers are chosen at random without replacement from 1 to 10. The probability that the minimum of the chosen number is 3, and their maximum is 7, is?

Three numbers are chosen at random without replacement from 1 to 10. The probability that the minimum of the chosen number is 3, and their maximum is 7, is?

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