Final answer:
The probability of all six tulips blooming as yellow flowers when picking and planting from eleven bulbs is 1 in 462. This is computed by recognizing only one possible combination for selecting six yellow bulbs out of six and dividing it by the total number of combinations for selecting any six bulbs out of eleven.
Step-by-step explanation:
The student is asking for the probability of selecting and planting six yellow tulip bulbs out of a total of eleven tulip bulbs, where there are six yellow and five pink bulbs. To find this probability, we need to use combinations to determine how many ways we can select six yellow tulips out of the six available. Since there is only one way to pick six yellow bulbs from six yellow bulbs, the numerator of our probability is 1.
Next, we calculate the total number of ways to pick any six bulbs out of the eleven without regard to color. This can be calculated by the combination formula C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, and k is the number of items to choose. For our case, this is C(11, 6). Therefore, the total number of combinations is 11! / (6! * 5!) = 462.
The probability of all six tulips blooming as yellow flowers is the ratio of the desired outcome (only one way to get six yellow tulips) to the total possible outcomes (462 ways to pick six tulips of any color), so the probability is 1 / 462.