Question

Question 4 Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Class X1 - Maths -Permutations and Combinations Page 148

Answer 1

Total number of digits = 5 { 1, 2, 3, 4 , and 5 }

—, —, — , —
number of ways to fill the unit place =5
number of ways to fill the ten place = 4
number of ways to fill the hundred place = 3
number of ways to fill the thousand place = 2

hence, by Fundamental principle of counting,
total number of ways = 5 × 4 × 3 × 2
= 120


again,
for even :
number of ways to fill the unit place = 2 { because 2 , 4 can be filled for even number }
number of ways to fill the tenth place = 4
number of ways to fill the hundred place = 3
number of ways to fill the thousand place = 2
by , fundamental principle of counting,
total number of ways = 2 × 4 × 3 × 2 = 48