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

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Anchit Jain Grade: 11

My question is:

How many 15 letter arrangement's of 5 A's , 5 B's , 5 C's have no A's in the first 5 letters , no B's in next 5 letters , and no C's in the last 5 letters

7 years ago

Answers : (1)

Aman Bansal
592 Points

dear Anchit,

at first it appears that first 5 letters are to be chosen from Bs and Cs, so there are 10 * 9 * 8 * 7 * 6 ways to satisfy the condition that there would be no As in first 5. but then next 5 is dependent on what happens in first 5 letter slots, so its "more complicated" i get that then it says "suppose that we only use 5 Bs in the first 5 places. there are 5! ways to do this. Then all C's must go in the 2nd 5 places and all A's must go in last 5 places. there are a total of (5!)^3 choices when we use only Bs in the first 5 places.. if we use 4 Bs and 1 C in the first 5 places, there are (5 1) [written vertically so its a parenthese with 5 on top of the one] ways they can be chosen..." then it goes on to explain all the other scenarios. what i don't get is, why are there 5! ways to "use only Bs in the first 5 places? isn't BBBBB the same as BBBBB? so shouldn't it be 5C5... not 5!? because if they're going to distinguish between BBBBB, then why are they suddenly doing 5 choose 1 ways in the "if we use 4 Bs and 1 C in the first 5 places?" unless the vertical parentheses is the 5 P 1..


Don’t forget to approve the answer if it is beneficial to you… !!

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar.. 


7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete AIPMT/AIIMS Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details