The rose bush challenge: a gardener sells 10 different varietie of rose bush. a gardener wishes to buy 6 rose*

*bushes, all of different varieties.





i) calculate the number of ways she can make her selection.





this is the tough hard part:





Of the 10 varieties, 3 are pink, 5 are red and 2 are yellow. Calculate the number of ways in which her selection of 6 rose bushes could contain:





i) no pink rose bush


ii) at least one rose bush of each color

The rose bush challenge: a gardener sells 10 different varietie of rose bush. a gardener wishes to buy 6 rose*
i) no pink rose bush....





ommit pink, so there are only 7 flowers... so :


7C6 = 7! / (6! * 1!) = 7 ways..





ii) at least one rose bush of each color...





(2C1 * 3C1 * 5C4) + (2C2 * 3C1 * 5C3) + (2C2 * 3C2 * 5C2) + (2C2 * 3C3 * 5C1)


= (2 * 3 * 5) + (1 * 3 * 10) + (1 * 3 *10) + (1 * 1 * 5)


= 30 + 30 + 30 + 5


= 95





there are 95 selection ^_^

flower