Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
21.0k views
in Permutations by (65.5k points)
recategorized by

How many 4 digit even numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6 

(a) when digits can be repeated 

(b) when digits are not repeated

1 Answer

+1 vote
by (65.2k points)
selected by
 
Best answer

(a) When digits can be repeated: 

The units place can be filled by the 4 even numbers in ways. For each of these the remaining places can be filled in 6, 7, 7 ways 

∴ the numbers are 6 × 7 × 7 × 4 = 1176.

(b) When digits are not repeated: 

Case 1: O is filled in units place thousandth place can be filled in 6 ways 

∴ the number of ways = 6 × 5 × 4 × 1 = 120 ways.

Case 2: O is not filled in units place and not in thousandth place also :: the units place can be filled in 3 ways (2 or 4 or 6) 

∴ The number of ways = 5 × 5 × 4 × 3 = 300 ways 

∴ The total number of ways = 300 + 120 = 420 ways

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...