LUSAK A APEX MEDICAL UNIVERSITY
PREMEDICAL SCIENCES
DEPARTMENT OF MATHEMATICS
12/10/2021
TUTORIAL SHEET 4
1. A code word is to consist of 2 distinct English alphabets followed by two distinct numbers
between 1 and 9.for example PD 92.
i) How many such codes are there?
ii) How many of them end with and even integer
2. It has been decided that the flag of the newly developed forum in the form of three blocks
Each colored differently .if there are five different colors to choose from, how many such designs
are possible
3. How many words (with or without meaning) of three distinct English alphabets are there?
4. In how many ways can a consonant and a vowel be chosen out of the word GREAT?
5. A number lock on the suitcase has three wheels, each labeled with 10 digit from 0 to 9.if
opening of the lock is a particular sequence of three digits with no repeats. How many such
sequences are possible?
6. A student must take a course on a modern language, social science, natural science and English.
There are five possible modern languages, three natural science, and four social sciences.
Every student must take the same English course.in how many ways can a student select his
course of study.
7. How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not
repeated
8. State the differences between the terms permutation and combination.
9. Evaluate the following
30!
i)
28!
ii) (30!)2! +6!
iii)
1
1
2
1
1
+ 4! + 5!
3!
3𝑥
10. If 9!+10! = 11! Find the value of x𝑒 −𝑖𝜔𝑡
11. If (𝑛 + 𝑧)! = 60[(𝑛 − 1)!] Find the value of n.
12. If nP5 = 60 nP2, find the value of n.
13. Find p(n-1,3):p(n,4)=1:9 find the value n.
14. In how many ways can the word PEMUTATIONS be arranged if
a. If the word start with P and end with S.
b. Consonants are together
15. 10 guest are to be seated in a row. Three of them are be seated together of the remaining 7, 2
do not wish to seat side by side. Find the number of possible arrangements.
16. How many different words can be formed with the letters of the word CHINYANTA?
i) In how many of these C and H are never together..
ii) How many of these begin with C and end with T.
17. In how many ways can the product x𝑦 2 𝑧 2 be written without using exponents.
18. If 2nC3:nC3=11:1 ,find n.
19. Find n if nCn-4=5.
20. Evaluate the following.
i) (50) ii) (88) + (84) iii) 60 (𝑛𝑛)
21. In how many ways can a team of 11 players be selected out of a 16 players
a. If two particular players are always to be included
b. If one particular player is to excluded
c. If two particular players are to be selected and one particular player
rejected.
22. In an examination, tony has to answer 4 questions from each section. if there are 7,8 and 9
questions in section A,B and C respectively.in how many ways can this be done.
23. From a group of 10 men and 6 women. five persons are to selected to form a committee so that
at least 3men are selected on the committee.in how many ways can it be done.
24. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be
formed?
25. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be
drawn from the box, if at least one black ball is to be included in the draw?
26.In how many different ways can the letters of the word 'DETAIL' be arranged in such a way
that the vowels occupy only the odd positions?