Question
Question: The number of ten digit numbers that contain only 2 & 3 as its digits but no any pairwise 3¢s joins ...
The number of ten digit numbers that contain only 2 & 3 as its digits but no any pairwise 3¢s joins together is
A
145
B
143
C
129
D
None
Answer
143
Explanation
Solution
When exactly one 3¢s & nine 2¢s are used then numbers possible = 10C1
When exactly two 3¢s & eight 2¢s are used then numbers possible =9C2
When exactly three 3¢s & seven 2¢s are used then numbers possible = 8C3
When exactly four 3¢s & six 2¢s are used then numbers possible = 7C4
When exactly five 3¢s & five 2¢s are used then numbers possible = 6C5
Adding all = 143