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Permutation and Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutation and Combinations3 Marks
Question
Match each item given under the column C1 to its correct answer given under the column C2.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of :
C1
C2
(a)
One book of each subject.
(i)
3968
(b)
At least one book of each subject.
(ii)
60
(c)
At least one book of English.
(iii)
3255
✓

Answer
C1
C2
(a)
One book of each subject.
(ii)
60
(b)
At least one book of each subject.
(iii)
3255
(c)
At least one book of English.
(i)
3968
Explanation:
We have 3 books of mathematics, 4 of physics and 5 on english
  1. One book of each subject = 3C1 × 4C1 × 5C1 × = 3 × 4 × = 60
  2. Alleast one book of each subject = (22 - 1) × (24 - 1) × (25 - 1) = 7 × 15 × 31 = 3255
  3. Atlest one book of english = (25 - 1) × 27 = 31 × 128 = 3968. Hence the required matching is

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