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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.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
C1
C2
(a)
4 letters are used at a time.
(i)
720
(b)
All letters are used at a time.
(ii)
240
(c)
All letters are used but the first is a vowel.
(iii)
360
✓

Answer
C1
C2
(a)
4 letters are used at a time.
(iii)
360
(b)
All letters are used at a time.
(i)
720
(c)
All letters are used but the first is a vowel.
(ii)
240
Explanation:
  1. 4 Letter are used at time $=^6\text{P}_4=\frac{6!}{2!}=360$
  2. All letters are used at time $^6\text{P}_6=6!=720$
  3. All letters are used but first letter is vowel $=2\times5!=2\times120=240$

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