Five numbers x 1 , x 2 , x 3 , x 4 , x 5 are randomly selected from the numbers 1 , 2 , 3 , … … , 18 and are arranged in the increasing order x 1 < x 2 < x 1 < x 4 < x 2 . The probability that x 2 = 7 and x 4 = 11 is

Question

Five numbers x 1 , x 2 , x 3 , x 4 , x 5 are randomly selected from the numbers 1 , 2 , 3 , &#8230; &#8230; , 18 and are arranged in the increasing order x 1 &#60; x 2 &#60; x 1 &#60; x 4 &#60; x 2 . The probability that x 2 = 7 and x 4 = 11 is

Aicharya · Accepted Answer

We know x 1 &#60; 7 &#60; x 3 &#60; 11 &#60; x 5 x 1 &#8712; 1 , 2 , 3 , 4 , 5 , 6 x 3 &#8712; 8 , 9 , 10 x 5 &#8712; 12 , 13 , 14 , 15 , 16 , 17 , 18 Required probability P = C 1 6 &#215; C 1 3 &#215; C 1 7 C 5 18 = 1 68

Five numbers x 1 , x 2 , x 3 , x 4 , x 5 are randomly selected from the numbers 1 , 2 , 3 , … … …

Solution

Five numbers x 1 , x 2 , x 3 , x 4 , x 5 are randomly selected from the numbers 1 , 2 , 3 , &#8230; &#8230; …

Solution

Five numbers x 1 , x 2 , x 3 , x 4 , x 5 are randomly selected from the numbers 1 , 2 , 3 , … … …