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Find the number of 4 -digit numbers that can be formed using t

Question

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?

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Owen Discussed

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?

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

4

digits can be selected in

_{5} C_{4}

ways

4

digits can be arranged in

4!

ways

so, the number of 4 digits number formed are

_{5} C_{4} \times 4! = 5 \times 4! = 5! = 120

for even number unit digit of the number has to be

2

4

unit digit of the number can be selected in

_{2} C_{1}

ways

number other than unit digit can be formed in

_{4} C_{3} \times 3!

ways

= 4 \times 6 = 24

ways

total number of even number will be

_{2} C_{1} \times 24 = 48

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Question Text	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?
Answer Type	Text solution:1
Upvotes	150