Question

4.
The number of 10-digit numbers such that the product of any two consecutive digits in the number is a
prime number, is​

Answer 1

Answer:

15 लाख की तीसरी क़िस्त मिलने पर सभी को बधाइयां

जिनको नहीं मिली वह अपनी उम्मीद और आलू संभाल के रखें !!

Answer 2

The number of ways are 2048.

Step-by-step explanation:

Consider the provided information.

We want the product of any two consecutive digits is a prime number it is possible if and only if when one of them is 1 and the other is a prime number.

That means every other number has to be 1.

The other digits have to be 2,3,5, or 7.

We need 10 digit numbers,

Case 1: Consider numbers of the form (1x)(1x)(1x)(1x)(1x),

Where x = 2,3,5, or 7. For each x we have 4 possible selections (2, 3, 5, 7).

So the number of possible ways are: = 4×4×4×4×4=1024

Case 2: Consider numbers of the form (x1)(x1)(x1)(x1)(x1).

For each x you have 4 possible selections (2, 3, 5, 7).

Thus, the Possible numbers ways are = 4×4×4×4×4=1024

Thus, total possible numbers = 1024+1024=2048

Hence, the number of ways are 2048.

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