Question

A veggie wrap at David's Deli is composed of 33 different vegetables and 22 different condiments wrapped up in a tortilla. If there are 66 vegetables, 66 condiments, and 55 types of tortilla available, how many different veggie wraps can be made

Answer 1

The answer is "
`7.21 * 10^(37)`".

Explanation:

`\to ^(n)_(C_r)=(n!)/(r!(n-r)!)`

`=^(66)_{C_(33)} * ^(66)_{C_(22)} * ^(55)_{C_(1)} \\\\=(66!)/(33! (66-33)!) * (66!)/(22! (66-22)!) * (55!)/(1! (55-1)!)\\\\=(66!)/(33! (33)!) * (66!)/(22! (44)!) * (55!)/(1! (54)!)\\\\=(66!)/(33! (33)!) * (66!)/(22! (44)!) * (55* 54!)/(1! (54)!)\\\\=(66!)/(33! (33)!) * (66!)/(22! (44)!) * 55\\\\= 7219428434016265740 * 182183167981760400* 55\\\\`

`= 7.21 * 10^(18) * 1.82*10^(17)* 55\\\\= 7.21 * 10^(35) * 1.82* 55\\\\=721.721 * 10^(35)\\\\=7.21* 10^(37)`