Question

Counting question

Answer 1

The number of ways in which \(3\) numbers are chosen at random
from \(\{1,2,3,\cdots ,10\}\) without replacement such that minimum is \(3\) or maximum is \(7\) is ?

Answer 2

So you have to choose 3 and 7 definitely, and so you get to choose among 4, 5, 6 in the middle.

{3, 4, 7}
{3, 5, 7}
{3, 6, 7}

Answer 3

no,no it is 3 \(\huge or \) 7

Answer 4

That's OK. We still had to calculate that.\[|A \cup B| = |A| + |B| - |A \cap B|\]We just calculated the third part.

Answer 5

ok i get that

Answer 6

You can similarly calculate \(|A|\) and \(|B|\).

Answer 7

\(\large A=\left(\dbinom{8}{3}-\dbinom{7}{3}\right)\)

\(\large B=\left(\dbinom{7}{3}-\dbinom{6}{3}\right)\)

is this correct ?

Answer 8

yes

Answer 9

thnks

Answer 10

better represented as 7C2 and 6C2 but it's the same