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 $=20$,
$(\because 0$ 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
$$ =4+20+100+250=374 $$
