2. (a) (i) How many different five-digit whole numbers may be formed from the di

ID: 3230231 • Letter: 2

Question

2. (a) (i) How many different five-digit whole numbers may be formed from the digits 1, 3, 5, 7, and 9 if repeated digits are allowed?

(ii) How many of the numbers so formed are greater than 78,000?

(iii) How many of the numbers so formed are divisible by 2?

(iv) How many of the numbers so formed are divisible by 5?

(b) (i) How many different five-digit whole numbers may be formed from the digits 1, 3, 5, 7, and 9 if digits may not be repeated?

(ii) How many of the numbers so formed are divisible by 3?

Answer:

2. (a) (i) How many different five-digit whole numbers may be formed from the digits 1, 3, 5, 7, and 9 if repeated digits are allowed?

Number of ways= 5*5*5*5*5 =3125

(ii) How many of the numbers so formed are greater than 78,000?

First two numbers are 79 or 97 or 99 and remaining three numbers are 1,3,5.

3*5*5*5 =375 ways.

(iii) How many of the numbers so formed are divisible by 2?

All are ending with odd number.

Numbers so formed are divisible by 2 is 0.

(iv) How many of the numbers so formed are divisible by 5?

Numbers end with 5 are divisible by 5.

5*5*5*5*1 =625

(b) (i) How many different five-digit whole numbers may be formed from the digits 1, 3, 5, 7, and 9 if digits may not be repeated?

5*4*3*2*1 =120 ways

(ii) How many of the numbers so formed are divisible by 3?

1+3+5+7+9 =25 is not divisible by 3.

Numbers so formed are divisible by 3 is 0 .

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