How many 5-digit numbers can be formed by using digits 1, 2, 3, 4, 5 if 2 and 3 cannot come together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 72
It is easier to count the numbers in which 2 and 3 are together and take them away from all the arrangements of the five digits (each digit used once).
All arrangements of 1, 2, 3, 4, 5: \(5!=120\)
2 and 3 together, treated as one block:
The block and 1, 4, 5 make 4 items: \(4!=24\) arrangements
The block itself can be 23 or 32: \(24\times2=48\)
2 and 3 not together: \(120-48=\) 72