# Combination and Permutation

1.3-1 There are total 8 digits and we wants to choose 4 digit from 8 digits for locks. Since in the number lock, we may choose combinations of repeated numbers. Thus first digit can be chosen from 8 ways. Since other second, third and fourth digits can be chosen from 8 ways .

1.3-2 since there are 4 Orchids we choose exactly three different orchid then total no. of ways i.e. first orchid can be chosen by 4 ways (due to different colors), similarly remaining orchids can be chosen by 3 and 2 respectively.

1.3-3

a. Two letter followed by a four-digit integer. There are 26 letters and 10 digits. since repetition is allowed then we may choose these two letters by 26 ways and 0 is a leading numbers thus first digit can be chosen by 10 ways and similarly others can be chosen by 10 ways respectively.

b. Two letter followed by a four-digit integer. There are 26 letters and 10 digits. since repetition is allowed then we may choose these these letters by 26 ways and 0 is leading numbers thus first digit can be chosen by 10 ways and similarly others can be chosen by 10 ways respectively.

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Solution is attached.

1.3-1 There are total 8 digits and we wants to choose 4 digit from 8 digits for locks. Since in the number lock, we may choose combinations of repeated numbers. Thus first digit can be chosen from 8 ways. Since other second, third and fourth digits can be chosen from 8 ways .

Thus Total no of ways = 8.8.8.8 = 4096 ...

#### Solution Summary

This solution shows step-by-step calculations to determine the total number of ways a specific sequence can be created in multiple combination and permutation scenarios.