you spin each spinner and find the sum. how many different sums are possible?

you spin each spinner and find the sum. how many different sums are possible?

you spin each spinner and find the sum. how many different sums are possible?

Answer

Explanation:

Step1: List all combinations

Let the numbers on the first spinner be (4,5,6,7), the second spinner be (2,3) and the third spinner be (4,5). We find all possible sums by taking one - number from each spinner. For the first spinner value (4):

  • With second - spinner value (2) and third - spinner value (4), sum (=4 + 2+4=10)
  • With second - spinner value (2) and third - spinner value (5), sum (=4 + 2+5 = 11)
  • With second - spinner value (3) and third - spinner value (4), sum (=4+3 + 4=11) (already counted above)
  • With second - spinner value (3) and third - spinner value (5), sum (=4+3 + 5=12)

For the first spinner value (5):

  • With second - spinner value (2) and third - spinner value (4), sum (=5 + 2+4=11) (already counted)
  • With second - spinner value (2) and third - spinner value (5), sum (=5 + 2+5 = 12) (already counted)
  • With second - spinner value (3) and third - spinner value (4), sum (=5+3 + 4=12) (already counted)
  • With second - spinner value (3) and third - spinner value (5), sum (=5+3 + 5=13)

For the first spinner value (6):

  • With second - spinner value (2) and third - spinner value (4), sum (=6 + 2+4=12) (already counted)
  • With second - spinner value (2) and third - spinner value (5), sum (=6 + 2+5 = 13) (already counted)
  • With second - spinner value (3) and third - spinner value (4), sum (=6+3 + 4=13) (already counted)
  • With second - spinner value (3) and third - spinner value (5), sum (=6+3 + 5=14)

For the first spinner value (7):

  • With second - spinner value (2) and third - spinner value (4), sum (=7 + 2+4=13) (already counted)
  • With second - spinner value (2) and third - spinner value (5), sum (=7 + 2+5 = 14) (already counted)
  • With second - spinner value (3) and third - spinner value (4), sum (=7+3 + 4=14) (already counted)
  • With second - spinner value (3) and third - spinner value (5), sum (=7+3 + 5=15)

Step2: Count unique sums

The unique sums are (10,11,12,13,14,15).

Answer:

6