There are few boxes labelled with $1,2,4,5,7,8,9$ respectively. How many ways are there to choose $5$ boxes and arranges the boxes in a row...
a) if only one box labelled with even number can be selected?
b) if all the box labelled with even number can be selected?
Can you guys help me solve this question?
There are 3 even numbered boxes and 4 odd numbered boxes.
a) If only one box labelled with even number can be selected, then the number of ways of choosing the boxes is (3C1) * (4C4) = 3. The number of ways to arrange these is 5! since the 5 boxes can be arranged in 5P5 ways. Hence, required answer shall be 3*5! = 360.
b) If all the even numbered boxes can be selected, then you have cases where you select 1 even 4 odd, 2 even 3 odd and 3 even 2 odd. These can be chosen in (3C1*4C4) + (3C2*4C3)+(3C3*4C2) ways, which equals 21. Again arranging them is 5! because for each case you have 5P5 ways of arranging them. Hence, the answer here will be 21*5! = 2520.