1. there are 4 parcels and 5 post offices . in how many different ways can the parcels be sent by registred post? 2. 12 students compete in a race . In how many ways first 3 prizes can be given? 3. In how many ways can 6 persons be seated in a row? 4. How many 9 digit numbers of different digits can be formed? 5. How many odd numbers less than 1000 can be formed by using the digits 0,3,5,7 when repetition of digits is not allowed? 6.seial numbers for an item produced in factory are to be made using 2 leters followed by 4 digits(0-9). If the letters are to be taken from 6 letters of english alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?

							
Dear Kurma,
1) Choose the 4 places for the consonants that is 7C4, the order on the consonants is given LGBR... and there is only one way to put the vowels as well AEA thus the total ways to rearrange without changing the relative order of vowel and consonant is 7C4=35

2)Each parcel has 5 possibilities to be sent therefore there are 5^4 ways to send the parcels...

3) as boys and girls should alternate there are only two ways to put the boys and girls

G-B-G-B-G-B-G-B-G-B

B-G-B-G-B-G-B-G-B-G

for each of this two there are as you said (5!)^2 way to arrange the boys and girls into this formation

so the answer is 2 (5!)^2

4) there are m+2 parallels in each of the directions of the side of the original parallelogram any two of the parallels in one direction and any two of the other direction will form a parallelogram

thus the answer is [(m+2)C2]^2
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