four darts are thrown at a dart board .if all four darts hit the board,how many different point total are possible
bullseye 9
second circle 7
third circle 4
outer circle 1
I can't see any other way than listing the possible cases and finding the total score for each case. Using the first letter of each outcome, we could have
BBBB -- 36
BBBS -- 34
BBBT -- 31
BBBO -- 28
BBSS -- 32
BBTT -- 26
BBOO -- 20
BBST -- 29
BBSO --
BBTO
etc, watch for duplication of totals
40
To calculate the number of different point totals that are possible when four darts are thrown at a dartboard, we can use the concept of combinations. Since there are four darts and each dart can either hit the bullseye, second circle, third circle, or the outer circle, there are a total of 4 options for each dart.
To find the number of combinations, we start by considering the number of ways the darts can hit the board:
1. For the first dart, there are 4 possible options (bullseye, second circle, third circle, or outer circle).
2. For the second dart, since it can also hit any of the 4 options, there are 4 possible options as well.
3. The same applies to the third dart and the fourth dart.
To find the total number of combinations, we multiply the options together:
Total number of combinations = 4 (options for first dart) x 4 (options for second dart) x 4 (options for third dart) x 4 (options for fourth dart)
Total number of combinations = 4^4 = 256
Therefore, there are 256 different point totals that are possible when four darts are thrown at the dartboard.