Statement – 1 : The number of selections of four letters taken from the word PARALLEL must be 15  
Statement-2: If Maths books have 4 different volumes each volume have 5 copies and physics book have 5 different volumes each have 4 copies then total no. of selecting at least one book of each subject is  $(6^4-1)$  $(5^5-1)$

 $1\text{'}p,2\text{'}A,1R,3\text{'}L,1E$
4 diff :  $5_{C_4}=5$
3 alike of 1 kind & 1 diff =  $1_{C_1}{.4}_{C_1}=4$
2 alike of 1 kind & 2 diff =  $2_{C_1}{.4}_{C_2}=12$
2 alike of 1 kind & 2 diff of 2nd kind =  $2_{C_2}=1$
                  Total = 22
 $5M_1,5M_2,5M_3,5M_4,4P_1,4P_2,4P_3,4P_4,4P_5$
no.of ways of selecting at least one Maths is  $\mathrm{6.6.6.6}-1$
no.of ways of selecting atleast one Physics book is  $\mathrm{5.5.5.5.5}-1$