To find the greatest number of identical arrangements the florist can make with the given amounts of lilies (60) and daisies (36), we need to determine how many arrangements can be formed based on the combinations provided.
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6 arrangements with 10 lilies and 6 daisies:
- Total lilies used: 6 arrangements * 10 lilies/arrangement = 60 lilies
- Total daisies used: 6 arrangements * 6 daisies/arrangement = 36 daisies
- This combination uses all available flowers.
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6 arrangements with 6 lilies and 10 daisies:
- Total lilies used: 6 arrangements * 6 lilies/arrangement = 36 lilies
- Total daisies used: 6 arrangements * 10 daisies/arrangement = 60 daisies
- This combination does not use all available flowers (only uses 36 lilies).
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12 arrangements with 10 lilies and 6 daisies:
- Total lilies used: 12 arrangements * 10 lilies/arrangement = 120 lilies
- Total daisies used: 12 arrangements * 6 daisies/arrangement = 72 daisies
- This combination exceeds the available amount of both flowers.
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12 arrangements with 5 lilies and 3 daisies:
- Total lilies used: 12 arrangements * 5 lilies/arrangement = 60 lilies
- Total daisies used: 12 arrangements * 3 daisies/arrangement = 36 daisies
- This combination uses all available flowers.
Now, comparing the valid combinations:
- The first combination (6 arrangements with 10 lilies and 6 daisies) and the fourth combination (12 arrangements with 5 lilies and 3 daisies) both utilize all of the flowers.
- However, the second option does not use all the lilies, and the third option exceeds the available blooms.
Between the first and the fourth, the first provides the arrangement with 10 lilies and 6 daisies can be made 6 times, whereas the fourth one enables the florist to make 12 arrangements with 5 lilies and 3 daisies.
Therefore, the greatest number of identical arrangements that can be made with available flowers is:
12 arrangements with 5 lilies and 3 daisies.