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Permutation and Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutation and Combinations5 Marks
Question
Match each item given under the column C1 to its correct answer given under the column C2.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
C1
C2
(a)
how many numbers are formed.
(i)
840
(b)
how many numbers are exactly divisible by 2.
(ii)
200
(c)
how many numbers are exactly divisible by 25.
(iii)
360
(d)
how many of these are exactly divisble by 4.
(iv)
40
✓

Answer
C1
C2
(a)
how many numbers are formed.
(i)
840
(b)
how many numbers are exactly divisible by 2.
(iii)
360
(c)
how many numbers are exactly divisible by 25.
(iv)
40
(d)
how many of these are exactly divisble by 4.
(ii)
200
Explanation:
  1. Total of 4 digit number formed with 1, 2, 3, 4, 5, 6, 7 $=\ ^7\text{P}_4=\frac{7!}{(7-4)!}=\frac{7\times6\times5\times4\times3!}{3!}=840$
  2. When anumber is divisible by $2=4\times5\times6\times3=360$
  3. Total number which are divisible by 25 = 40
  4. Total number which are divisible by 4 (last two digits is divisible by 4) = 200

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