leslie has 17 tomato plants that she wants to plant in rows. she will put 2 plants in some rows and 1 plant in others. how many different ways can she plant the tomato plants?
No rows of twos
one row of twos
two rows of twos
three rows of twos
four rows of twos
five rows of twos
six rows of twos
seven rows of twos
eight rows of twos
17 in 1 in 2 = 20 becauese like this
17 in 1 in 2 = 20 wirte so than you have to make no rows so 11111111111111111111=20
36
To find out how many different ways Leslie can plant the tomato plants, we can consider the two possible options for each row: either 2 plants or 1 plant.
Let's break it down into two cases:
Case 1: Rows with 2 plants:
In this case, Leslie needs to create rows with 2 plants each. To determine the number of rows with 2 plants, we can divide the total number of tomato plants (17) by 2, since each row contains 2 plants.
17 ÷ 2 = 8 rows (with 2 plants each)
Case 2: Rows with 1 plant:
In this case, Leslie needs to create rows with 1 plant each. Each row will have 1 plant, and we can place the remaining tomato plants in any of the rows with 1 plant.
Since we already have 8 rows with 2 plants each, the number of rows with 1 plant can range from 0 to 8. Therefore, we have 9 possible options for the number of rows with 1 plant.
Now, to determine the number of ways Leslie can arrange the tomato plants, we need to find the total number of combinations by multiplying the number of options in each case.
Total ways = Number of options in Case 1 × Number of options in Case 2
Total ways = 8 rows × 9 options
Total ways = 72
Therefore, Leslie can plant the tomato plants in 72 different ways.