Paper 4: Fundamentals of Business Mathematics & Statistic

2.44 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Solution :

If one boy takes his seat anywhere in a round table, then remaining 4 boys can take seats in 4! = 24 ways.

In each of these 24 ways, between 5 boys, if 5 girls take their seats then no two girls will be side by side. So

in this way 5 girls may be placed in 5 places in 5! = 120 ways.

Again the first boy while taking seat, may take any one of the 10 seats, i.e., he may take his seat in 10 ways.

Hence, reqd. number ways = 24 × 120 × 10 = 28,800.

SELF EXAMINATION QUESTIONS

1. Find the value of : (i)^10 P 2 (ii)^10 P 0 (iii)^10 P 10 [Ans. (i) 90 (ii) 1 (iii) 10 !]


2. Find the value of n : nP 4 = 10 ́ n–1P 3 [Ans. 10]


3. Find the value of r : (i)^11 P3r = 110 (ii)^7 Pr = 2520 [Ans. (i) 2 (ii) 5]


4. Find n : (i) if nP 5 : nP 3 = 2 : 1 (ii) nP 3 ́ n+2P 3 = 5 : 12 [Ans. (i) 5 (ii) 7]


5. Prove that “CALCUTTA” is twice of “AMERICA” in respect of number of arrangements of letters.
   OBJECTIVE QUESTIONS


6. There are 20 stations on a railway line. How many different kinds of single first-class tickets must be
   printed so as to enable a passenger to go from one station to another? [Ans. 380]


7. Four travellers arrive in a town where there are six hotels. In how many ways can they take their
   quarters each at a different hotel? [Ans. 360]


8. In how many ways can 8 mangoes of different sizes be distributed amongst 8 boys of different ages so
   that the largest one is always given to the youngest boy? [Ans. 5040]


9. Find the number of different number of 4 digits that can be formed with the digits 1, 2, 3, 4, 5, 6, 7 ; the
   digits in any number being all different and the digit in the unit place being always 7. [Ans. 120]


10. How many different odd numbers of 4 digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7 ; the digits
    in any number being all different? [Ans. 480]


11. How many number lying between 1000 and 2000 can be formed from the digits 1, 2, 4, 7, 8, 9 ; each
    digit not occurring more than once in the number? [Ans. 60]


12. Find the number of arrangements that can be made out of the letters of the following words :
    (a) COLLEGE
    (b) MATHEMATICS [Ans. (a) 1260 ; (b) 49, 89,600]


13. In how many ways can the colours of a rainbow be arranged, so that the red and the blue colours are
    always together? [Ans. 1440]


14. In how many ways 3 boys and 5 girls be arranged in a row so that all the 3 boys are together?
    [Ans. 4320]


15. Find how many words can be formed of the letters in the word FAILURE so that the four vowels come
    together. [Ans. 576]


16. In how many ways can 7 papers be arranged so that the best and the worst papers never come
    together? [Ans. 3600]


17. In how many ways can the colours of the rainbow be arranged so that red and blue colours are
    always separated? [Ans. 3600]