How many codes of 9 symbols can be formed by using the integers 1, 2, 3, 4, 5, 6 and letters a, b,

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29 Mar 2010 Code with 9 symbols?

How many codes of 9 symbols can be formed by using the integers 1, 2, 3, 4, 5, 6 and letters a, b, c, if
the 3 letters are necessarily taken together.

OPtion

1) 720
2) 5040
3) 30240
4) 362880
5) 120
6) 610
7) 7
8) 42
9) 4320
10) 3024

Solution

Suppose the set of 3 letters is a symbol, Then total symbols = 7

Methods for arranging these 7 symbols = 7*6*5*4*3*2*1 = 5040

Methods for arranging 3 letters = 3*2*1 = 6

Hence total number of codes formed = 5040*6 = 30240

Correct Option: 3 Best Solution (6)

HARMEET KAUR   14 years AGO

7!*3!= 30240

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Dr.Dipin Singh   14 years AGO

7*3!*6!= 30240

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Dr. Divya   14 years AGO

7!*3!= 30240

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ASHOK ROY   14 years AGO

Among 9 symbols we have to form codes keeping the 3 letters together which means that there will be 7 symbols if we decide to keep the 3 letters together. Then 7 symbols can be arranged in 7!=5040 ways. The 3 letters can be arranged in 3! ways=6 The total number of ways =5040*6=30240 ways

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Khanna   14 years AGO

3!*6!*7 = 30240

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Siddharth Gupta   14 years AGO

answer will be 7!*3!

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