Question

If 4 Maths books are selected from 6 different Maths different English books, how many ways can the seven om Maths books and 3 English books are chosen from 5 he seven books be arranged on a shelf: (a) If there are no restrictions? (4) • (3) - 76 = 756.000 (b) If the 4 Maths books remain together? (4) . (5.4!= 3400 (c) a Maths book is at the beginning of the shelf? (d) Maths and English books alternate. (9):13).46.3.- 216000 (e) A Maths is at the beginning and an English book is in the middle of the shelf

Answer 1

Answer:

Please see the answer below

Step-by-step explanation:

a. Since there’s no restrictions .Therefore , the number of ways = 7!*150 = 756000

b. The number of ways such that the 4 math books remain together

The pattern is as follows:  MMMMEEE, EMMMMEE, EEMMMME, and EEEMMMM

Where M = Math’s Book and E= English Book.  

Number of ways = 4!*8!*4*150= 86400 ways.

c. The number of ways such that  math book is at the beginning of the shelf

The number of ways = 6!*4*150 = 432000

d. The number of ways such that  math and English books alternate

The number of ways = 150*4!*3! =2160 ways

e.  The number of ways such that math is at the beginning and an English book is in the middle of the shelf. The number of ways = 4*3*5!*150 =216000 ways.

Answer 2

a)The number of 7 books to arrange with no restriction are 756000.

b)The number of ways to arrange the books keeping 4 math book together are 86400.

c) Total number of ways to arrange the 7 books keeping the a Math book is at the beginning of the shelf are 432000.

d)Total number of ways to arrange the 7 books keeping the math and English books alternate are 2160.

e)Total number of ways to arrange the 7 books keeping A Math is at the beginning and an English book is in the middle of the shelf 216000.

Given-

Total math books are 6.

Total math books selected are 4.

Total English books are 5.

Total English books selected are 3.

The number of ways to arrange the number of ways to select 4 math books form 6 math and 4 English books form 5 English books

$=\dfrac{6\times5}{2} \times\dfrac{5\times4\times3}{3\times2}$

$=150$

a)if there are no restrictions-As there is no restriction, thus we have total 7 books to arrange.The number of ways this 7 books can be arranged,

$=7!\times 150$

$=7\times6\times5\times4\times3\times2\times1\times150$

$=756000$

Thus, the number of 7 books to arrange with no restriction are 756000.

(b) The 4 Math books remain together-Let M is Math book and E is English book. Now we have to arrange the 7 books in shelf in which 4 math books should be together. Total number of ways to arrange when 4 math book can be find by identifying the pattern which is EEMMMME, EMMMMEE, MMMMEEE, EEEMMMM. This pattern will be used for all the 7 maths books and all the 4 English books. So the number of ways to arrange the books keeping 4 math book together,

$=4!\times8!\times 4\times 150$

$=86400$

Thus ,the number of ways to arrange the books keeping 4 math book together are 86400.

(c) a Math book is at the beginning of the shelf-We can keep 4 math book at first place one by one. We have total 6 math book so the arrangement will be change for each math book replacement. Thus total number of ways to arrange the 7 books keeping the a Math book is at the beginning of the shelf,

$=6!\times 4\times 150$

$432000$

(d) Math and English books alternate-The pattern will be MEMEMEM for the 4 math book and 1 English book. We have only 1 way and there are English and math book can replace with remaining books. Thus total number of ways to arrange the 7 books keeping the math and English books alternate,

$=4!\times3!\times1\times150$

$=2160$

(e) A Math is at the beginning and an English book is in the middle of the shelf- Total number of ways to arrange the 7 books keeping A Math is at the beginning and an English book is in the middle of the shelf-

$=5!\times 4\times3\times150$

$216000$

Hence,

a)The number of 7 books to arrange with no restriction are 756000.

b)The number of ways to arrange the books keeping 4 math book together are 86400.

c) Total number of ways to arrange the 7 books keeping the a Math book is at the beginning of the shelf are 432000.

d)Total number of ways to arrange the 7 books keeping the math and English books alternate are 2160.

e)Total number of ways to arrange the 7 books keeping A Math is at the beginning and an English book is in the middle of the shelf 216000.

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