Question

(d) 997 are *** The number of even numbers greater than 300 that the digits 1,2,3,4,5 without can be formed with repetition is (a) 110 (b) 112 (c) 111 (d) None of these lenne 924 h

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3-digit numbers: Must begin with ( 3,4,5, ) and must end with ( 2, ) or ( 4 . ) So if the first digit is 3 or ( 5, ) the last digit can be 2 or ( 4, ) and the 2 nd digit can be any of the 3 remaining digits: ( 2^{*} 2^{*} 3=12 . ) If the first digit is ( 4, ) then the last digit has to be 2 , and the 2 nd can be any of the 3 remaining: ( 1^{*} 1^{*} 3=3.12+3=15 ) total such 3 -digit numbers. 4 -digit numbers: The last digit has to be 2 or ( 4 . ) Then the first digit can be any of the 4 remaining digits, the 2 nd has 3 choices, and the 3 rd has ( 2: 2^{*} 4^{*} 3^{*} 2=48 ) such numbers. 5-digit numbers: Again, the last digit has to be 2 or ( 4, ) then the first has 4 options, the 2 nd has ( 3, ) the 3 rd has 2 and the 4 th has ( 1: 2^{*} 4^{*} 3^{*} 2^{*} 1=48 ) such numbers. Numbers with more than 5 digits require replication, and those with less than 3 aren't bigger than ( 300, ) so that's all of the options. ( 48+48+15=111 ) total such numbers.