In the annual picnic for STA 201 course teachers, 11 faculties (including a pair of twins, Snigdho and Mugdho) have been selected for a game of musical chair. (A game where all the participants have to sit on chairs arranged in circular fashion). a. How many ways can all those 11 faculties be arranged at the beginning of the game of musical chair? b. If Snigdho and Mugdho are determined about not sitting beside each other in the first round, how many ways can they sit so that they do not have to sit on adjacent chairs?
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.
In the annual picnic for STA 201 course teachers, 11 faculties (including a pair of twins, Snigdho
and Mugdho) have been selected for a game of musical chair. (A game where all the participants
have to sit on chairs arranged in circular fashion).
a. How many ways can all those 11 faculties be arranged at the beginning of the game of musical
chair?
b. If Snigdho and Mugdho are determined about not sitting beside each other in the first round,
how many ways can they sit so that they do not have to sit on adjacent chairs?
c. What is the probability that Snigdho and Mugdho will not be adjacent to each other?
[Hint: Probability of an
Total no of possible outcomes
]
d. After 5 teachers being eliminated from the game, in how many ways can the remaining
teachers be arranged in circular fashion?
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