Question

WILL CHOOSE BRAINIEST How many 6-digit numbers, formed using each digit from 1 to 6 exactly once, are divisible by: a.)5 b.)6 c.)12 d.)25

Answer 1

D) 25 tell me if I did it righ

Answer 2

Answer:

a) divisible by  5:  120 numbers

b) divisible by  6:    360 numbers

c) divisible by  12:     192 numbers

d) divisible by  25:    24 numbers

Step-by-step explanation:

6-digit  numbers => the numbers have the form abcdef

a.) divisible by  5

f = {5}

a  5 values;   b  4 values, c  3 values,  d  2 values ,   e  1 value, f 1 value

=> 5 * 4 * 3 * 2 * 1 * 1 = 120 numbers

b.) divisible by  6

f = {2; 4; 6}

a  5 values;   b  4 values, c  3 values,  d   2 values,   e 1 value, f  3 values

=> 5 * 4 * 3 * 2 * 1 * 3 = 360 numbers

c.) divisible by  12

ef =  {12; 16; 24; 32; 36; 52; 56; 64}

a  4 values;   b  3 values, c  2 values,  d   1 value,   ef  8 values

=> 4 * 3 * 2 * 1 * 8 =192 numbers

d.) divisible by  25

ef =  {25}

a  4 values;   b  3 values, c  2 values,  d   1 values,   ef  1 value

=> 4 * 3 * 2 *1*1 = 24 numbers