The first marble can go in any of the four pockets and so can the second and third marble.
Hence the total number of ways that three marbles can go in four pockets is 4 × 4 × 4 = 64 .
(n – 1) ! will not be divisible by n only if n is a prime number so the prime numbers between 20 and 40 are23, 29, 31, 37 total value of n = 4.
A line can be drawn by joining any two of the points so
20C2
But 5 colinear points will only give one line
∴ total number of lines will be 20C2 – 5C2 + 1.
Single-Digit Nos. = 2;
2-Digit Nos. = 2 (Ways of selecting unit’s digit) x 3 (Ways of selecting ten’s digit as zero cannot be used) = 6; 3-digit Nos. = 2 (Ways of selecting unit’s digit) x 4 (Ways of selecting ten’s digit) x 3 (Ways of selecting hundred’s digit as zero cannot be used) = 24;
4-digit Nos. = 2 (Ways of selecting unit’s digit) x 4 (Ways of selecting ten’s digit) x 4 (Ways of selecting hundred’s digit) x 3 (Ways of selecting thousand’s digit as zero cannot be used) = 96;
∴Total = 2 + 6 + 24 + 96 = 128