How many three digit numbers can be formed using the digits 1,2,3,4,5,6,7 and 8 without repeating the digits and such that the tens digit is greater than the hundreds digit and less than the units digit?
A.
48
B.
56
C.
64
D.
72
Answers
Given : three digit numbers can be formed using the digits 1,2,3,4,5,6,7 and 8 without repeating the digit
Tens digit is greater than the hundreds digit and less than the units digit?
To Find : How many such numbers are possible
Solution:
Number is ABC
A < B < C
A = 1 B = 2 C can be in 6 ways ( 3 to 8)
A = 1 B = 3 C can be in 5 ways ( 4 to 8)
A = 1 B =7 C can be in 1 ways
Hence 6 + 5 + 4 + 3 + 2 + 1 = 21
if A = 2 Then 5 + 4 + 3 + 2 + 1 = 15
if A = 3 Then 4 + 3 + 2 + 1 = 10
if A = 4 Then 3 + 2 + 1 = 6 ways
if A = 5 then 2 + 1 = 3 ways
if A = 6 then 1 way
Hence total = 21 + 15 + 10 + 6 + 3 + 1 = 56
Hence 56 such numbers are possible
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how many three digit numbers which are neither divisible by 4 nor 5 is
brainly.in/question/13181275
Given : three digit numbers can be formed using the digits 1,2,3,4,5,6,7 and 8 without repeating the digit
Tens digit is greater than the hundreds digit and less than the units digit?
To Find : How many such numbers are possible
Solution:
Number is ABC
A < B < C
A = 1 B = 2 C can be in 6 ways ( 3 to 8)
A = 1 B = 3 C can be in 5 ways ( 4 to 8)
A = 1 B =7 C can be in 1 ways
Hence 6 + 5 + 4 + 3 + 2 + 1 = 21
if A = 2 Then 5 + 4 + 3 + 2 + 1 = 15
if A = 3 Then 4 + 3 + 2 + 1 = 10
if A = 4 Then 3 + 2 + 1 = 6 ways
if A = 5 then 2 + 1 = 3 ways
if A = 6 then 1 way
Hence total = 21 + 15 + 10 + 6 + 3 + 1 = 56
Hence 56 such numbers are possible
Learn More:
brainly.in/question/20707237
00) All numbers which are divisible by 8 must also be divisible by 4 ...
brainly.in/question/17508568
how many three digit numbers which are neither divisible by 4 nor 5 is
brainly.in/question/13181275