How many even numbers of 5 digits without repetition can be formed with the digits 1,2 3 4 and 5?
The correct option is D Show
312 Even numbers can be formed by placing either 0 or 2 or 4 in the rightmost digit. _ _ _ _ 0 _ _ _ _ 2 _ _ _ _ 4 So, let us consider all the 3 cases separately. Case 1: Rightmost digit is 0 Leftmost digit can be filed with 1 or 2 or 3 or 4 or 5 So, number if ways of filling leftmost digit = 5 As 2 digits are already used, the next position can be filled with either of the 4 digits. Proceeding in this manner, the next 2 digits can be filled in 3 and 2 ways respectively −|5−|4−|3_0|2 So, the number of possible numbers = 5×4×3×2 = 120 Case 2: Rightmost digit is 2 _ _ _ _ 2 Available digits 0,1,3,4,5 Out of these 5 digits leftmost digit can be filed with 1 or 3 or 4 or 5 Proceeding in this manner, the next 2 digits can be filled in 3 and 2 ways respectively. −|4−|4−|3_2|2 So, the number of possible numbers = 4×4×3×2 = 96 Case 3: Rightmost digit is 4 −|4−|4−|3_4|2 Number of possible numbers = 4×4×3×2 = 96 ∴ the total number of arrangements = 120 + 96 + 96 = 312 How many 5 digit even numbers can be formed using the digits 1,2 3 4 5 exactly once?∴ the total number of arrangements = 120 + 96 + 96 = 312.
How many 5 digit numbers can be formed from the digits 1,2 3 4 5 using the digits without repetition 6 marks I how many of them are even?Therefore, there will be 60 distinct 5 - digit numbers.
How many 5 digit numbers can make using 5 digits without repeating?In their numeric form, these numerals have a total of 5 digits. Given: 5- digit numbers starting with 5 without repeating numbers from 0-5. Therefore, possibility of 5 digit numbers are 1 × 4 × 4 × 4 × 4 = 256. Hence, only 256 5-digit numbers can be made starting with 5 without repeating the digits from 0-5.
How many 5 digit numbers are there with no digit being repeated?Therefore, the number of 5-digit numbers that can be formed by using the digits 0, 1, 2,…..,7 is 5880. Hence, option D is the correct answer.
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