Question

The number of 4 digit numbers greater than 5,000 can be formed out of the digits 3,4,5,6

and 7(No. digit is repeated). The number of such ​

Answer 1

Answer:

to make a 4 digit number greater than 5000, we have 3 choices (5,6,7) for our thousands place.

similarly, for our hundred place we have 4 choices (3,4,5/6/7,5/6/7) and then 3&2.

so the total number of possibilities will be 3x4x3x2=72

these will be : (just for insight)

{5347,5376,5437,.......7643}

also, all 5 digit numbers formed from thr digits will be greater than 5000 so it will be 5p5=5!=120

summing up the total number of natural numbers formed from the digits 3,4,5,67, with out repetion ,and which are greater than 5000&192.

now for the even case ,we need to have an even number (here 4,6)at the ones place

there for we will consider two cases each for 4-5 digits numbers.

case 1- 4 has pre occupied the ones place in 4 digits numbers

now we have to arrange 4 number in to 3 places such that the complete thing is still greater than 5000.

thus 3 choices (5,6,7) for the thousands place 3(3,,5/6/7,5/6/7) for the hundreds and 2(3/5/6/7,3/5/6/7)for the tens, giving us 18 numbers.

case 2:6 has preoccupied the ones place in the 4 digit number.

this time we will have 2x3x2=12 numbers.

Now by similar arguments for the 5 digits numbers, we get a total of 2x4!=48 numbers.

we thus end up with a total of 78 even numbers and hence also 114 odd numbers.

hope that helped.