How many distinct 5 digit numbers can be formed using the digits 3, 2,

1.	How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5.
Answer» 5 digit numbers are to be formed from 2, 3, 2, 3, 4, 5. Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5 Number of such numbers = \(\frac{5!}{2!}+\frac{5!}{2!}=5!=120\) Case II: Numbers are formed from 2, 2, 3, 3 and any one of 4 or 5 Number of such numbers = \(\frac{5!}{2!2!}+\frac{5!}{2!2!}=60\) Required number of numbers = 120 + 60 = 180

How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5.

Answer»

5 digit numbers are to be formed from 2, 3, 2, 3, 4, 5.

Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5

Number of such numbers = \(\frac{5!}{2!}+\frac{5!}{2!}=5!=120\)

Case II: Numbers are formed from 2, 2, 3, 3 and any one of 4 or 5

Number of such numbers = \(\frac{5!}{2!2!}+\frac{5!}{2!2!}=60\)

Required number of numbers = 120 + 60 = 180