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Permutations MCQ1( 2,3,5,1,7,9 , four digits, even numbers)

Permutations MCQ1: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}

a) 60             b) 360            c) 120           d) 240

Solution:

 

Here first we know that a four digit number is like 1023, 4568, 7894 etc

we read these numbers in the following way;

drawit diagram 1

 

If we read 4586 we will read;

Thousands Hundred Tens Unit
4 5 8 6

 

i- 4 thousand 5 hundreds and 86

Also we notice that if any number is having ‘2’ at unit digit slot –  then it is called even because it will be divisible by ‘2’

i-e numbers like 35792, 1532 etc are even numbers!

 

Question is how many even numbers we can make from given digits!

Out of given digits the digit ‘2’ if placed at unit place (first slot of unit digit) in a four digit number, then we will get even number i-e we have to think about , ‘tens, ‘hundreds’  and ‘thousand ‘ slots only where we have to put remaining five digits i-e 3,5,1,7  and 9  —-  to be put in three slots in different ways ! i-e there will be permutation of 5 things in 3 slots.

Formula for permutations of ‘n’ things and ‘r’ slots is;

\[ ^n\rm P_r= \frac {n!}{(n-r)!} \]

So the number of ways of putting these five digit in three slots will be;

\[ ^5\rm P_3=\frac {5!}{(5-3)!} \]

\[ =\frac{5\times 4 \times 3 \times 2}{(2 \times 1)}=60 \]

 

So, 60  four digit even numbers making is possible with given digits!

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