Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

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
`        How many Number of 7digit natural number in which both 2&3 are  present as digits if no 2`s  are consecutive in any number?`
2 years ago

Arun
23353 Points
```							Dear student I’ll presume you mean 7-digit natural numbers with only 2s and 3s, but with no 2s adjacent to each other.For example, 2323232 would be fine, but 3223332 would not be.One way to do this is with a recurrence relation.Let A(n) = the number of n-digit natural numbers with only 2s and 3s, but with no 2s adjacent to each other.Consider the last digit. Either it’s a 2 or a 3. If it’s a 3, then the first n-1 digits can be any valid number, because any valid number followed by a 3 is valid. By definition, there are A(n-1) of these.But the last digit could also be a 2. In this case, the n-1 digit could not be a 2, otherwise you’d have two 2s together. So the n-1 digit must be a 3. Now, the first n-2 digits can be any valid number. By definition, there are A(n-2) of these.So this gives us the recurrence relation A(n) = A(n-1) + A(n-2). We’ll need two boundary conditions, since this is a 2nd order recurrence relation.A(1) = 2, because either 2 or 3 is valid. A(2) = 3 because 23, 32, and 33 are valid 2-digit numbers.Now we can use these to compute A(7), which is what we want. So:A(3) = A(2) + A(1) = 3 + 2 = 5A(4) = A(3) + A(2) = 5 + 3 = 8A(5) = A(4) + A(3) = 8 + 5 = 13A(6) = A(5) + A(4) = 13 + 8 = 21 and finallyA(7) = A(6) + A(5) = 21 + 13 = 34And that’s our answer. RegardsArun (askIITians forum expert)
```
2 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »

### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions