A class contains $b$ boys and $g$ girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then $b + 3g$ is equal to $\_\_\_\_$.

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is $\_\_\_\_$.

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is $\_\_\_\_$.

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is $\underline{\hspace{1cm}}$.

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is $\_\_\_\_$

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to : (1) 179 (2) 177 (3) 181 (4) 175

Group A consists of 7 boys and 3 girls, while group $B$ consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :
(1) 8750
(2) 9100
(3) 8925
(4) 8575

A convenience store packages three building block models (A, B, C) and five character figurines ($a, b, c, d, e$), totaling eight toys, into two bags for sale. Each bag contains four toys, and the packaging follows these principles: (I) A and $a$ must be in the same bag. (II) Each bag must contain at least one building block model. (III) $d$ and $e$ must be in different bags. Based on the above, select the correct options.
(1) Each bag must contain at least two character figurines
(2) B and C must be in different bags
(3) If B and $d$ are in the same bag, then C and $e$ must be in the same bag
(4) If B and $d$ are in different bags, then $b$ and $c$ must be in different bags
(5) If $b$ and $c$ are in different bags, then B and C must be in the same bag

Divide the 50 positive integers from 1 to 50 equally into groups A and B, with 25 numbers in each group, such that the median of group A is 1 less than the median of group B. How many ways are there to divide them?
(1) $C_{25}^{50}$
(2) $C_{24}^{48}$
(3) $C_{12}^{24}$
(4) $\left(C_{12}^{24}\right)^{2}$
(5) $C_{24}^{48} \cdot C_{12}^{24}$

A florist has roses of 5 different colors in large quantities and 2 types of vases. A customer wants to buy a total of 3 roses of 2 different colors and 1 vase.
In how many different ways can this customer make the purchase?
A) 15
B) 20
C) 25
D) 40
E) 50

A school's basketball team has a total of 8 players, two of whom are brothers. 5 of these players will be selected to be in the starting lineup.
In how many different ways can a selection be made such that both brothers are in this lineup?
A) 20 B) 24 C) 30 D) 36 E) 40