aike: g the first letter N: 8 ways g the third letter 2 ways Cannot be the same

Question

aike: g the first letter N: 8 ways g the third letter 2 ways Cannot be the same as the first N: 7 ways Cannot be the same as the second, but can be the same as the first 8-7-7 = 392 possible code words 5J Ho habet under the three different conditions stated in Example 52 w many 4-letter code words are possible using the first Solve Problems 7-10 two ways: (A) using a tree diagram, and using the multiplication principle. 7. How many ways can 2 coins turn up-heads, H, or tails, T-if the combined outcome (H, T) is to be distinguished from the outcome (T, H)? 8. How many 2-letter code words can be formed from the first 3 letters of the alphabet if no letter can be used more than once?

Explanation / Answer

Question 8

Two letter word of initital 3 letters, which are A,B and C and both of them must be different.

so possible combinations are : AB,BA,AC,CA,BC,CB

so total 6 combinations.

Question 13

3 letter codes from A,B,C,D and E and

(i) no letter is repeated, combinations = 5P3 = 5 * 4 * 3 = 60

(iii) Letter are repeated = 53= 125

(iii) adjacent letters must be replaced = 5 * 4 * 4 = 80 [ as we have 5 numbers to pick from and 4 number of second number and 4 is for third number ]

Question 14

4 letter codes from A,B,C,D,E,F and G

(i) no letter is repeated, combinations = 7P4 = 7 * 6 * 5 * 4 = 840

(iii) Letter are repeated = 74= 2401

(iii) adjacent letters must be replaced = 7 * 6 * 6 * 6= 1512 [ as we have 7 numbers to pick from for first number and 4 number of second number and 4 is for third number ]

Question 35

5 choices of color, 3 choices of transmission, 4 types of interior, 2 type of engine.

Total possibilities = 5 * 3 * 4 * 2 = 120

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