8/12/2019 IB HL Counting Binomial Questions

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IB Math HL Counting Principle and Binomial Expansions

1. Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table

for a meeting. Mr Black and Mrs White must not sit together.

Calculate the number of different ways these six eole can sit at the table without Mr Black

and Mrs White sitting together.

2. !n how many ways can six different coins be di"ided between two students so that each student

recei"es at least one coin#

3. $ow many four%digit numbers are there which contain at least one digit

4. ' committee of four children is chosen from eight children. (he two oldest children cannot both

be chosen. )ind the number of ways the committee may be chosen.

. ' team of fi"e students is to be chosen at random to take art in a debate. (he team is to bechosen from a grou of eight medical students and three law students. )ind the robability that

*a+ only medical students are chosen

*b+ all three law students are chosen.

!. (here are - seats in a row in a waiting room. (here are six eole in the room.

*a+ !n how many different ways can they be seated#

*b+ !n the grou of six eole, there are three sisters who must sit next to each other.

!n how many different ways can the grou be seated#

". (wel"e eole tra"el in three cars, with four eole in each car. /ach car is dri"en by its owner.

)ind the number of ways in which the remaining nine eole may be allocated to the cars. *(he

arrangement of eole within a articular car is not rele"ant+.

#. Gi"en that

*- 0x+1*- 0 ax+

2- 0 bx0 -x

30 ............... 0 a

2x

--,

find the "alues of a, b 4.

$. )ind the coefficient ofx5in the exansion of *3 0 &x+

-, gi"ing your answer as a whole number.

1%. (he coefficient ofx in the exansion of

5

3

-

+

ax

x

is &5

. )ind the ossible "alues of a.

11. )ind the coefficient ofx&in the binomial exansion of

6

3

-7-

x

.

12. *a+ Write down the term inx

r

in the exansion of *x

0h+

n

, where

r

n

,n

0

.

*b+ $ence differentiatexn, n

0, from first rinciles.

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8/12/2019 IB HL Counting Binomial Questions

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*c+ 8tarting from the resultxnx

n9 -, deduce the deri"ati"e ofx

n, n

0.

13. :etermine the first three terms in the exansion of *-; 3x

+

1

*-0x

+

5

in ascending owers ofx

.

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