John, Jim, Jack and Joe have formed a band consisting of 4 instruments (drums, piano, guitar, flute). If John, Jim and Jack can play all 4 instruments, but Joe can play only drums, piano and guitar, how many different arrangements are possible? What if John can play all four instruments, Jim can play drums, flute and piano and Jack and Joe can each play only piano and guitar?
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.
John, Jim, Jack and Joe have formed a band consisting of 4 instruments (drums, piano, guitar, flute).
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If John, Jim and Jack can play all 4 instruments, but Joe can play only drums, piano and guitar, how many different arrangements are possible?
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What if John can play all four instruments, Jim can play drums, flute and piano and Jack and Joe can each play only piano and guitar?
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