Suppose there are 21 identical spheres in a box with numbers 1 to 6 written on them. The number of spheres with number n is up to n. (n = 1,2, ..., 6) For example, there is 1 ball with number 1, 2 balls with number 2, 3 balls with number 3, and so on. It is as if we choose from inside the box. Write down its number and put it back in the box. If we are allowed to repeat this 11 times. 1) Calculate the distribution function to obtain the Hayes ball with the number 6. 2) What is the probability that ball number 3 will be selected 3 times? 3) What is the probability that ball number 6 will be selected 3 times?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Suppose there are 21 identical spheres in a box with numbers 1 to 6 written on them. The number of spheres with number n is up to n. (n = 1,2, ..., 6) For example, there is 1 ball with number 1, 2 balls with number 2, 3 balls with number 3, and so on.
It is as if we choose from inside the box. Write down its number and put it back in the box. If we are allowed to repeat this 11 times.
1) Calculate the distribution
2) What is the
3) What is the probability that ball number 6 will be selected 3 times?
Step by step
Solved in 7 steps
