A squad of 20 boys, which includes 2 sets of twins , is available for selection for a cricket team of 11 players. Calculate the number of different teams that can be selected if one set of twins is selected but neither twin from the other set is selected.
Is this a combination?
yes
first select one of the pairs of twins .... C(2,1) = 2
So in effect 2 players are chosen but 4 players are taken out of the picture, we need 9 more from the remaining 16 ----- C(16,9)
number of teams = 2*C(16,9) = ....
Oh, you're taking me back to my math days! Let's see if I can juggle these numbers for you.
First, let's pick one set of twins. We have 2 options for that. However, we can't pick both twins from the other set, so we have to choose only one of them, which gives us 1 option.
Now we need to choose the remaining 9 players from the remaining 17 boys, excluding the twins we've already picked. This can be calculated using a combination:
C(17, 9) = 17! / ((17-9)! * 9!) = 24310
So, the number of different teams that can be selected is 2 (for the set of twins) multiplied by 1 (for choosing one twin from the other set) multiplied by 24310 (for the remaining 9 players).
In total, we have: 2 x 1 x 24310 = 48,620 different teams.
That's a whole lot of cricket-playing clowns!
Yes, this problem involves combinations. In combinatorics, the order of selection does not matter, which is the case when forming a team.
Yes, this is a combination problem. We need to select a cricket team of 11 players from a squad of 20 boys, which includes 2 sets of twins. We are given the condition that one set of twins must be selected, but neither twin from the other set can be selected.
To calculate the number of different teams that can be selected, we can break the problem down into three parts:
1. Selecting one set of twins: There are 2 options for selecting one set of twins.
2. Selecting the remaining 9 players from the remaining 16 boys: Since we cannot select either twin from the other set, we are left with 16 - 2 = 14 players to choose from. We need to select 9 players from this group, which can be done in C(14, 9) = 2002 ways. Here, C(n, r) represents the number of combinations of selecting r items from a group of n items.
3. Combining the choices from parts 1 and 2: To calculate the total number of different teams, we need to multiply the choices from both parts. Therefore, the total number of different teams that can be selected is 2 * 2002 = 4004.
So, there are 4004 different teams that can be selected if one set of twins is selected but neither twin from the other set is selected.