Calculating Impatiens Colour Combinations
The problem asks for the number of ways to select 6 distinct colours from a total of 9 distinct colours. Since the order of the colours does not matter, this is a combination problem.
Understanding Combinations
We need to find the number of combinations of choosing 6 items (colours) from a set of 9 distinct items (Impatiens species). The formula for combinations is:
$C(n, k) = \binom{n}{k} = \frac{n!}{k!(n-k)!}$
Where:
- $n$ is the total number of items available (9 species).
- $k$ is the number of items to choose (6 species).
Step-by-Step Calculation
- Identify the values for $n$ and $k$: $n=9$, $k=6$.
- Apply the combination formula:
$C(9, 6) = \binom{9}{6} = \frac{9!}{6!(9-6)!}$
- Simplify the expression:
$C(9, 6) = \frac{9!}{6!3!} = \frac{9 \times 8 \times 7 \times 6!}{6! \times (3 \times 2 \times 1)}$
- Cancel out $6!$:
$C(9, 6) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1}$
- Calculate the result:
$C(9, 6) = \frac{504}{6} = 84$
Therefore, there are 84 possible colour combinations.
Important Questions from Combinations
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ?
Bob is studying the effect of coral and sponge species on reef ecosystems using experiments in artificial square tanks. In each tank, he places 3 species of corals and 2 species of sponges. If there are 6 species of corals and 5 species of sponges to choose from, the minimum number of tanks required to test all combinations of 3 coral and 2 sponge species is _______
(Answer in integer)
- Ten teams participate in a tournament. Every team plays each of the other teams twice. The total number of matches to be played is
- The number of ways in which a supervisor can choose four workers out of 10 equally competent workers is ________.
- In a box, there are 5 green balls and 10 blue balls. A person picks 6 ballsrandomly. The probability that the person has picked 4 green balls and 2 blueballs is
