SATHEE: Permutations and Combinations 3 Question 4

Permutations and Combinations 3 Question 4

4. The number of natural numbers less than 7,000 which can be formed by using the digits $0, 1, 3, 7, 9$ (repitition of digits allowed) is equal to

(2019 Main, 9 Jan II)

(a) 374

(b) 375

(c) 372

(d) 250

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Answer:

Correct Answer: 4. (a)

Solution:

Using the digits $0, 1, 3, 7, 9$

number of one digit natural numbers that can be formed $= 4$ ,

number of two digit natural numbers that can be formed $= 20$ ,

$(∵ 0$ can not come in Ist box)

number of three digit natural numbers that can be formed $= 100$

and number of four digit natural numbers less than 7000 , that can be formed $= 250$

( $∵$ only 1 or 3 can come in Ist box)

$∴$ Total number of natural numbers formed

$= 4 + 20 + 100 + 250 = 374$

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Permutations and Combinations 3 Question 4

4. The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repitition of digits allowed) is equal to

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4. The number of natural numbers less than 7,000 which can be formed by using the digits $0, 1, 3, 7, 9$ (repitition of digits allowed) is equal to