Numbers of Different Numerals, Circular Permutation, With Repetitions

Competency Evaluation on Capability. Froblem Form:
1. The numbers which are consist of three different numerals and its value is less than 500, will be formed by the numerals 3, 4, 5, 6. the number of the numbers which is formed =…
A. 4 B. 6 C. 10 D. 12 E. 18
Answer: D, Explanation:

different numerals

2. The numbers which are consist of three numerals and its value is less than 300, will be formed by the numerals 2, 3, 4, 5. If the numerals can be repeated, then the number of the numbers which is formed =…
A. 9 B. 16 C. 18 D. 27 E. 54
Answer: B, Explanation:

repeated numerals

3. Seven students sit rounding a circular table. the number of ways for the 7 students to round the circle table is equal to …
A. 720 B. 360 C. 180 D. 90 E. 45
Answer: A, Explanation:

(7-1)!=6!=6∙5∙4∙3∙2∙1=720

4. From seven students, three of them will be called one by one to do sport test. the number of ways to call the three students is equal to …
A. 840 B. 210 C. 70 D. 35 E. 21
Answer: B, Explanation:
calling one by one as a sequence. Use permutation.

use permutation

5. From a class will be chosen 5 male and 3 female to form a group for jogging competition. If in that class there are 8 male, and 12 female, then the number of ways to form the group =….
A. 220 B. 276 C. 286 D. 56 E. 12320
Answer: E, Explanation:

combination male female

6. If nP4=42∙nP2 then nP3=⋯
A. 4 B. 21 C. 42 D. 84 E. 504
Answer: E, Explanation:

get n from permutation

7. A student is asked to solve 7 from 10 problems are provided. If froblem number 1 to 5 must be solved, then the number of choices for students to solve tne problem =…
A. 3 B. 5 C. 8 D. 10 E. 20
Answer: D, Explanation:

the number of choices

8. If 3∙(n+1)C3=7/2(n2+n) then nC5=⋯
A. 56 B. 50 C. 48 D. 46 E. 26334
Answer: E, Explanation:

get n from combination

9. The number of different arrangements which can be formed from the letters in word CARAWAWAN is equal to …
A. 5670 B. 5760 C. 6570 D. 6750 E. 7560
Answer: E, Explanation:
Remember permutation with repetition item(s).

permutation with repetition

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