Question

Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?

a) 6
b) 15
c) 20
d) 36

Answer 1

There are 20 combinations of the six known quarks that are possible if all combinations are allowed.

Step-by-step explanation:

In this case, we need to find the number of combinations of three quarks out of the six known quarks. Since we are looking for combinations and not permutations, we can use the combination formula. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects chosen.

Using this formula, we can calculate the number of combinations of three quarks out of the six known quarks: C(6, 3) = 6! / (3!(6-3)!) = 6! / (3!3!) = 6 × 5 × 4 / (3 × 2 × 1) = 20.

Therefore, the answer is c) 20 combinations of the six known quarks are possible if all combinations are allowed.