Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

total number of 4 digit numbers such that the sum of the digits is odd,is (a)2720 (b)5040 (c)3680 (d)4500

total number of 4 digit numbers such that the sum of the digits is odd,is



  • (a)2720

  • (b)5040

  • (c)3680

  • (d)4500

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear shaurya sinha

sum of digit will be odd if there is only one odd number or 3 odd number

we have 1,3,5,7,9 odd digit and 0,2,4,6,8 even digit

Case 1    ,only one odd number

  a )  odd digit at first place can be filled by 5 ways

 and  rest 3 position can be filled by 5*5*5 ways

 b  )  odd digit other than 1st palce can be filled by 3C1 *5

  and first position can be filled by 4 ways

 and rest two position can be filled by 5*5 ways

       total ways  =5*5*5*5 +3*5*4*5*5

                       =2125 ways

case 2 ,exactly 3 odd number

  a) even digit at first palec can be filled by 4 ways

         and  rest 3 position can be filled by 5*5*5 ways

b  )  even digit other than 1st palce can be filled by 3C1 *5

  and  rest 3 position can be filled by 5*5*5 ways

Total number of ways =4*5*5*5 + 3*5*5*5*5

                                =2374 ways


so total ways =2125+2374 =4500


Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin

   

 


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free