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:

  1. 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 $=20$,

$(\because 0$ 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 $=250$

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

$\therefore$ Total number of natural numbers formed

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



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