Question

There are six periods in each working day in a school in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant . Total arrangements possible is?

A
210
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B
1800
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C
360
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D
120
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E
1500
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Solution

The correct option is A 210Each of the arrangements which can be made by taking some or all of a number of things is called a permutation.There are 5 subjects,Hindi,English,Maths,Science and Social studies.There are 6 periods.The first period can be allotted to any of the five subjects.That is, there are 5 different ways of allotting the first period.Now, one subject has been allotted.The second period can be allotted to any of the four subjects.That is, there are 4 different ways of allotting the second period.Now, two subjects has been allotted.The third period can be allotted to any of the three subjects.That is, there are 3 different ways of allotting the third period.Now, three subjects has been allotted.The fourth period can be allotted to any of the 2 subjects.That is, there are 2 different ways of allotting the fourth period.Now, four subjects has been allotted.The fifth period can be allotted to any of the 1 subject.That is, there is only one way of allotting the fifth period.Now, five subjects has been allotted.Thus,by the principle of counting there are =5×4×3×2×1=120 different ways to allot 5 periods.That is total number of arrangements=(6−1)(5×4×3×2×1)=5×120=600 arrangements

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