The average number of pairs of consecutive integers in a randomly select subset of 5 distinct integers from 1 to 30 is 570,024
The average number of pairs of consecutive integers in a randomly select subset of 5 distinct integers from 1 to 30 is expressed using the formula;
n = [tex]4 \cdot \frac{25}{30C_5}[/tex]
According to the combination formula:
[tex]30C_5=\frac{30!}{25!5!}\\30C_5 =\frac{30\times29\times28\times27\times 26}{5\times4\times3\times2}\\30C_5 =\frac{17,100,720}{120}\\30C_5 =142,506[/tex]
n = 4* 142,506
n = 570,024
Hence the average number of pairs of consecutive integers in a randomly select subset of 5 distinct integers from 1 to 30 is 570,024
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