Permutations And Combinations Question 298
Question: The number of 4 digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is [AMU 2001]
Options:
A) 1225
B) 1252
C) 1522
D) 750
Correct Answer: D 0,1,2,3,4,5,6,7 so that the each number contains digit 1 is Given that number is of 4 digits so the first digit can’t be 0. Let (i) first digit is (1).(ii) first digit is not 1 (i) First digit is 1 We pick 3 digits in order out of the remaining 7.6.5=210 possibilities. (ii) First digit is not 1 There are 6 ways to choose the first digit (2,3,4,5,6,7), 3 ways to place the digit 1 (hundreds, tens, ones)and 6.5 ways to choose the other digits So 6.3.6.5=540 possibilities ∴ total possibilities are 210+540=750 750 possibilities to choose the number that to each number contains digit 1
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Solution:
BETA
