Question Number 199310 by necx122 last updated on 01/Nov/23
$${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{a}\:{group}\:{of}\:\mathrm{3} \\ $$$${people}\:{born}\:{on}\:{the}\:{same}\:{day}\:{of}\:{the} \\ $$$${week}? \\ $$
Commented by AST last updated on 01/Nov/23
$$\mathrm{1} \\ $$
Answered by AST last updated on 01/Nov/23
$${There}\:{are}\:{only}\:\mathrm{7}\:{days}\:{in}\:{a}\:{week},{and}\:{the}\:{number} \\ $$$${of}\:{people}\:{has}\:{exceeded}\:{twice}\:{that}\:{amount}, \\ $$$${there}\:{must}\:{be}\:{a}\:{group}\:{of}\:{three}\:{people}\:{with}\:{the} \\ $$$${same}\:{day}. \\ $$
Commented by mr W last updated on 01/Nov/23
$${in}\:{following}\:{example}\:{there}\:{is}\:{no} \\ $$$${group}\:{of}\:{three}\:{people}\:{on}\:{the}\:{same}\:{day}: \\ $$$$\mathrm{1}\:{person}\:{on}\:{monday} \\ $$$$\mathrm{1}\:{person}\:{on}\:{tuesday} \\ $$$$\mathrm{2}\:{people}\:{on}\:{wednesday} \\ $$$$\mathrm{2}\:{people}\:{on}\:{thursday} \\ $$$$\mathrm{5}\:{people}\:{on}\:{friday} \\ $$$$\mathrm{7}\:{people}\:{on}\:{saturday} \\ $$$${no}\:{people}\:{on}\:{sunday} \\ $$
Commented by AST last updated on 01/Nov/23
$${We}\:{can}\:{pick}\:{a}\:{group}\:{of}\:\mathrm{3}\:{from}\:{the}\:\mathrm{5}\:{or}\:\mathrm{7}\:{on}\: \\ $$$${Friday}\:{or}\:{Saturday}\:{respectively} \\ $$
Commented by AST last updated on 01/Nov/23
$${The}\:{question}\:{didn}'{t}\:{state}\:“{of}\:'{only}'\:\mathrm{3}\:{people}'' \\ $$$${or}\:{a}\:{day}\:{with}\:\mathrm{3}\:{people}\:{only}. \\ $$
Commented by necx122 last updated on 01/Nov/23
unfortunately, I dont know the exact answer as my son just brought it to me. It's quite tricky but I think I can understand from the analysis from the solvings. Thank you sirs.