Problem Solving

teacher uses 10 flash cards numbered 1 through 10, to teach her students to order no correctely. she has students choose four flash cards randomly then arrange the cards in ascending order. one day, she removes the card numbered "2" and "4" from the deck of flsh cards. on that day, hoe many different correct arrangements of 4 randomly selected cards are possible?

70,210,336,840,1680

the formula for this is n!/(n-r)!r! - it is a combination problem becuase even though you have to order the cards there is only one way for you to correctly order any set of cards (in ascending order) - for example picking 3, 5, 6, 7 will result in only 1 correctly ordered set.

Thus, there are 8 cards available and she is choosing 4 therefore the formula is 8!/(8-4)! 4! which equals 70.

doesn't it means that we have to pick 2 and 4 as one of the number?

If the students choose a card snd and the teacher removes a card then that would mean those cards are not available for the students to choose, so I don't thimk it could mean thst you must choose those.