Question:
The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is
The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is
Updated On: Apr 14, 2024
- 450
- 432
- 454
- 436
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The Correct Option is B
Solution and Explanation
Given digits are 1, 2, 3, 4, 5, 6, 7.
Two even digits can be selected in $^{3}C_{2}$
Two odd digits can be selected in $^{4}C_{2}$ ways.
These selected 4 digits can be arranged in 4! ways.
$\therefore\, Total \,number\, of \,ways=^{4}C_{2}. ^{3}C_{2}. 4!$
$=6\times3\times24$
$=18\times24$
$=432$
Two even digits can be selected in $^{3}C_{2}$
Two odd digits can be selected in $^{4}C_{2}$ ways.
These selected 4 digits can be arranged in 4! ways.
$\therefore\, Total \,number\, of \,ways=^{4}C_{2}. ^{3}C_{2}. 4!$
$=6\times3\times24$
$=18\times24$
$=432$
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.